Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On the Six-dimensional Sphere with a Nearly Kählerian Structure

  • 7 Accesses

Abstract

In this paper, geometric properties of the six-dimensional sphere with a nearly Kählerian structure are described.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    A. Abu-Saleem and G. A. Banaru, “On some contact metric structures on hypersurfaces in a Kählerian manifold,” Acta Univ. Apulensis, 31, 179–189 (2012).

  2. 2.

    A. Abu-Saleem and M. B. Banaru, “Two theorems on Kenmotsu hypersurfaces in a W3-manifold,” Stud. Univ. Babeş–Bolyai. Math., 51, No. 3, 3–11 (2005).

  3. 3.

    A. Abu-Saleem and M. B. Banaru, “Some applications of Kirichenko tensors,” Anal. Univ. Oradea. Fasc. Mat., 17, No. 2, 201–208 (2010).

  4. 4.

    A. Abu-Saleem and M. B. Banaru, “On almost contact metric hypersurfaces of nearly Kählerian 6-sphere,” Malaysian J. Math. Sci., 8, No. 1, 35–46 (2014).

  5. 5.

    A. Abu-Saleem, A. Shihab, and M. B. Banaru, “On six-dimensional Kählerian and nearly Kählerian submanifolds of the Cayley algebra,” Anal. Univ. Oradea. Fasc. Mat., 21, No. 1, 29–39 (2014).

  6. 6.

    D. V. Alekseevsky, B. S. Kruglikov, and H. Winther, “Homogeneous almost complex structures in dimension 6 with semi-simple isotropy,” Ann. Glob. Anal. Geom., 46, 361–387 (2014).

  7. 7.

    V. I. Arnold, Mathematical Methods of Classical Mechanics [in Russian], M.: Nauka, (1989).

  8. 8.

    M. B. Banaru, Hermitian geometry of six-dimensional submanifolds of the Cayley algebra [in Russian], Ph.D. thesis, Moscow (1993).

  9. 9.

    M. B. Banaru, “Gray–Hervella classes of almost Hermitian structures on six-dimensional submanifolds of the Cayley algebras,” Nauch. Tr. Mosk. Ped. Gos. Univ., 36–38 (1994).

  10. 10.

    M. B. Banaru, “On six-dimensional submanifolds of the Cayley algebra,” Differ. Geom. Mnogoobr. Figur, 31, 6–8 (2000).

  11. 11.

    M. B. Banaru, “Six theorems on six-dimensional Hermitian submanifolds of the Cayley algebra,” Izv. Akad. Nauk Resp. Moldova. Ser. Mat., No. 3 (34), 3–10 (2000).

  12. 12.

    M. B. Banaru, “On six-dimensional Hermitian submanifolds of the Cayley algebra satisfying the g-cosymplectic hypersurfaces axiom,” Ann. Sofia Univ. St. K. Ohridski, 94, 91–96 (2000).

  13. 13.

    M. B. Banaru, “Two theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra,” J. Harbin Inst. Technol., 8, No. 1, 38–40 (2001).

  14. 14.

    M. B. Banaru, “A new characterization of the Gray–Hervella classes of almost Hermitian manifolds,” in: Proc. 8th Int. Conf. on Differential Geometry and Its Aplications, Opava, Czech Republic (2001), pp. 4.

  15. 15.

    M. B. Banaru, “Some theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra,” Mat. Vesnik, 53, No. 3-4, 103–110 (2001).

  16. 16.

    M. B. Banaru, “A note on six-dimensional G2-submanifolds of the Cayley algebra,” An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă. Mat., 47, No. 2, 389–396 (2001).

  17. 17.

    M. B. Banaru, “On spectra of some tensors of six-dimensional K¨ahlerian submanifolds of the Cayley algebra,” Stud. Univ. Babeş–Bolyai. Math., 47, No. 1, 11–17 (2002).

  18. 18.

    M. B. Banaru, “Two theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra,” Izv. Vyssh. Ucheb. Zaved. Ser. Mat., No. 1 (476), 9–12 (2002).

  19. 19.

    M. B. Banaru, “On Hermitian manifolds satisfying the axiom of U-cosymplectic surfaces,” Fundam. Prikl. Mat., 8, No. 3, 934–937 (2002).

  20. 20.

    M. B. Banaru, “Hermitian geometry of six-dimensional submanifolds of the Cayley algebra,” Mat. Sb., 193, No. 5, 3–16 (2002).

  21. 21.

    M. B. Banaru, “On nearly cosymplectic hypersurfaces in nearly Kählerian manifolds,” Stud. Univ. BabeşBolyai. Math., 47, No. 3, 3–11 (2002).

  22. 22.

    M. B. Banaru, “On Kenmotsu hypersurfaces in a six-dimensional Hermitian submanifolds of the Cayley algebra,” in: Proc. Int. Conf. “Contemporary Geometry and Related Topics,” Belgrade (2002), p. 5.

  23. 23.

    M. B. Banaru, “A note on six-dimensional G1-submanifolds of the octave algebra,” Taiwan. J. Math., 6, No. 3, 383–388 (2002).

  24. 24.

    M. B. Banaru, “Six-dimensional Hermitian submanifolds of the Cayley algebra and u-Sasakian hypersurface axiom,” Izv. Akad. Nauk Resp. Moldova. Ser. Mat., No. 2 (39), 71–76 (2002).

  25. 25.

    M. B. Banaru, “On totally umbilical cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra,” Acta Univ. Palacki Olomuc. Math., 41, 7–12 (2002).

  26. 26.

    M. B. Banaru, “On the type number of six-dimensional planar Hermitian submanifolds of the Cayley algebra,” Kyungpook Math. J., 43, No. 1, 27–35 (2003).

  27. 27.

    M. B. Banaru, “On cosymplectic hypersurfaces of six-dimensional Kählerian submanifolds of the Cayley algebra,” Izv. Vyssh. Ucheb. Zaved. Ser. Mat., No. 7 (494), 59–63 (2003).

  28. 28.

    M. B. Banaru, “On six-dimensional G2-submanifolds of the Cayley algebra,” Mat. Zametki, 74, No. 3, 323–328 (2003).

  29. 29.

    M. B. Banaru, “On Sasakian hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra,” Mat. Sb., 194, No. 8, 13–24 (2003).

  30. 30.

    M. B. Banaru, “On the type number of cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra,” Sib. Mat. Zh., 44, No. 5, 981–991 (2003).

  31. 31.

    M. B. Banaru, “On Kenmotsu hypersurfaces of six-dimensional Hermitian submanifolds of the Cayley algebra,” Differ. Geom. Mnogoobr. Figur, 34, 12–21 (2003).

  32. 32.

    M. B. Banaru, “On Kenmotsu hypersurfaces in a six-dimensional Hermitian submanifold of the Cayley algebra,” in: Proc. Int. Conf. “Contemporary Geometry and Related Topics,” Belgrade (2002), pp. 33–40.

  33. 33.

    M. B. Banaru, “On the Gray–Hervella classes of AH-structures on six-dimensional submanifolds of the Cayley algebra,” Ann. Sofia Univ. St. K. Ohridski, 95, 125–131 (2004).

  34. 34.

    M. B. Banaru, “On Kirichenko tensors of nearly K¨ahlerian manifolds,” J. Sichuan Univ. Sci. Eng., 25, No. 4, 1–5 (2012).

  35. 35.

    M. B. Banaru, “On some almost contact metric hypersurfaces of nearly Kählerian manifolds,” in: Proc. 20th Conf. on Applied and Industrial Mathematics, Chişinău (2012), pp. 16–17.

  36. 36.

    M. B. Banaru, “The U-Kenmotsu hypersurfaces axiom and six-dimensional Hermitian submanifolds of the Cayley algebra,” J. Sichuan Univ. Sci. Eng., 26, No. 3, 1–5 (2013).

  37. 37.

    M. B. Banaru, “Special Hermitian manifolds and the 1-cosymplectic hypersurfaces axiom,” Bull. Austr. Math. Soc., 90, No. 3, 504–509 (2014).

  38. 38.

    M. B. Banaru, “Kenmotsu hypersurface axiom for six-dimensional Hermitian submanifolds of the Cayley algebra,” Sib. Mat. Zh., 55, No. 2, 261–266 (2014).

  39. 39.

    M. B. Banaru, “On almost contact metric 1-hypersurfaces of Kählerian manifolds,” Sib. Mat. Zh., 55, No. 4, 719–723 (2014).

  40. 40.

    M. B. Banaru, “Almost contact metric hypersurfaces with type number 1 or 0 in nearly Kählerian manifolds,” Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 3, 60–62 (2014).

  41. 41.

    M. B. Banaru, “On almost contact metric hypersurfaces with type number 1 in six-dimensional Kählerian submanifolds of the Cayley algebra,” Izv. Vyssh. Ucheb. Zaved. Ser. Mat., No. 10, 13–18 (2014).

  42. 42.

    M. B. Banaru, “On almost contact metric hypersurfaces of NK-manifolds,” in: Proc. II Int. Conf. “Geometric Analysis and Its Applications, Volgograd (2014), pp. 14–17.

  43. 43.

    M. B. Banaru, “Geometry of six-dimensional almost Hermitian submanifolds of the algebra of octaves,” Itogi Nauki Tekh. Sovr. Mat. Prilozh. Temat. Obzory, 126, 10–61 (2014).

  44. 44.

    M. B. Banaru, “W4-manifolds and axiom of cosymplectic hypersurfaces,” Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 5, 34–37 (2015).

  45. 45.

    M. B. Banaru, “On almost contact metric 2-hypersurfaces in six-dimensional Kählerian submanifolds of the Cayley algebra,” in: Proc. Int. Conf. “Geometry Days in Novosibirsk–2015,” Novosibirsk (2015), pp. 9–10.

  46. 46.

    M. B. Banaru, “On almost contact metric 2-hypersurfaces in Kählerian manifolds,” Bull. Transilvania Univ. of Braşov. Ser. III. Math. Inform. Phys., 9 (58), No. 1, 1–10 (2016).

  47. 47.

    M. B. Banaru, “Axiom of Sasakian hypersurfaces and six-dimensional Hermitian submanifolds of the octave algebra,” Mat. Zametki, 99, No. 1, 140–144 (2016).

  48. 48.

    M. B. Banaru and G. A. Banaru, “A note on six-dimensional planar Hermitian submanifolds of the Cayley algebra,” Izv. Akad. Nauk Resp. Moldova. Ser. Mat., No. 1 (74), 23–32 (2014).

  49. 49.

    M. B. Banaru and G. A. Banaru, “On almost contact metric hypersurfaces of the six-dimensional sphere,” Sist. Komp. Mat. Prilozh., 16, 126–127 (2015).

  50. 50.

    M. B. Banaru and G. A. Banaru, “1-Cosymplectic hypersurfaces axiom and six-dimensional planar Hermitian submanifolds of the octonian,” SUT J. Math., 51, No. 1, 1–9 (2015).

  51. 51.

    M. B. Banaru and G. A. Banaru, “A note on almost contact metric hypersurfaces of the nearly Kählerian 6-sphere,” Bull. Transilvania Univ. Braşov. Ser. III. Math. Inform. Phys., 8 (57), No. 2, 21–28 (2015).

  52. 52.

    M. B. Banaru and V. F. Kirichenko, “Hermitian geometry of six-dimensional submanifolds of the Cayley algebra,” Usp. Mat. Nauk, 49, No. 1, 205–206 (1994).

  53. 53.

    F. Belgun and A. Moroianu, “Nearly Kählerian 6-manifolds with reduced holonomy,” Ann. Global Anal. Geom., 19, 307–319 (2001).

  54. 54.

    D. E. Blair, “Contact manifolds in Riemannian geometry,” Lect. Notes Math., 509, 1–145 (1976).

  55. 55.

    D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progr. Math., Birkhäuser, Boston–Basel–Berlin (2002).

  56. 56.

    J. Bolton, F. Dillen, B. Dioos, and L. Vrancken, “Almost complex surfaces in the nearly Kählerian S3× S3,” Tôhoku Math. J., 67, 1–17 (2015).

  57. 57.

    R. Brown and A. Gray, “Vector cross products,” Commum. Math. Helv., 42, 222–236 (1967).

  58. 58.

    E. Calabi, “Construction and properties of some 6-dimensional almost complex manifolds,” Trans. Am. Math. Soc., 87, No. 2, 407–438 (1958).

  59. 59.

    J. T. Cho and K. Sekigawa, “Six-dimensional quasi-Kählerian manifolds of constant sectional curvature,” Tsukuba J. Math., 22, No. 3, 611–627 (1998).

  60. 60.

    N. A. Daurtseva, “On the existence of a structure of the class G2 on a strictly nearly Kählerian six-dimensional manifold,” Vestn. Tomsk. Univ. Ser. Mat. Mekh., No. 6 (32), 19–24 (2014).

  61. 61.

    R. Deszcz, F. Dillen, L. Verstraelen, and L. Vrancken, “Quasi-Einstein totally real submanifolds of nearly Kählerian 6-spher,” Tôhoku Math. J., 51, 461–478 (1999).

  62. 62.

    M. Djoric and L. Vrancken, “Three-dimensional CR-submanifolds in the nearly Kählerian 6- sphere with one-dimensional nullity,” Int. J. Math., 20, No. 2, 189–208 (2009).

  63. 63.

    B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry. Methods and Applications [in Russian], Nauka, Moscow (1986).

  64. 64.

    N. Ejiri, “Totally real submanifolds in a 6-sphere,” Proc. Am. Math. Soc., 83, 759–763 (1981).

  65. 65.

    H. Endo, “On the curvature tensor of nearly cosymplectic manifolds of constant Phi-sectional curvature,” An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat., 51, No. 2, 439–454 (2005).

  66. 66.

    H. Endo, “Remarks on nearly cosymplectic manifolds of constant Phi-sectional curvature with a submersion of geodesic fibers,” Tensor, N.S., 66, 26–39 (2005).

  67. 67.

    H. Endo, “On nearly cosymplectic manifolds of constant Phi-sectional curvature,” Tensor, N.S., 67, 323–335 (2006).

  68. 68.

    H. Endo, “Some remarks of nearly cosymplectic manifolds of constant Phi-sectional curvature,” Tensor, N.S., 68, 204–221 (2007).

  69. 69.

    S. Funabashi and J. S. Pak, “Tubular hypersurfaces of the nearly Kählerian 6-sphere,” Saitama Math. J., 19, 13–36 (2001).

  70. 70.

    G. Gheorghiev and V. Oproiu, Varietăţi diferentiabile finit şi infinit dimensionale, Vols. I, II, Academia RSR, Bucureşti (1976, 1979).

  71. 71.

    A. Gray, “Some examples of almost Hermitian manifolds,” Ill. J. Math., 10, No. 2, 353–366 (1966).

  72. 72.

    A. Gray, “Six-dimensional almost complex manifolds defined by means of three-fold vector cross products,” Tôhoku Math. J., 21, No. 4, 614–620 (1969).

  73. 73.

    A. Gray, “Vector cross products on manifolds,” Trans. Am. Math. Soc., 141, 465–504 (1969).

  74. 74.

    A. Gray, “Almost complex submanifolds of the six sphere,” Proc. Am. Math. Soc., 20, 277–280 (1969).

  75. 75.

    A. Gray, “Nearly Kählerian manifolds,” J. Differ. Geom., 4, 283–309 (1970).

  76. 76.

    A. Gray, “The structure of nearly Kählerian manifolds,” Math. Ann., 223, 223–248 (1976).

  77. 77.

    A. Gray and L. M. Hervella, “The sixteen classes of almost Hermitian manifolds and their linear invariants,” Ann. Mat. Pura Appl., 123, No. 4, 35–58 (1980).

  78. 78.

    Li Haizhong, “The Ricci curvature of totally real 3-dimensional submanifolds of the nearly Kählerian 6-sphere,” Bull. Belg. Math. Soc. Simon Stevin, 3, 193–199 (1996).

  79. 79.

    Li Haizhong and Wei Gouxin, “Classification of Lagrangian Willmore submanifolds of the nearly Kählerian 6-sphere S6(1) with constant scalar curvature,” Glasgow Math. J., 48, 53–64 (2006).

  80. 80.

    H. Hashimoto, “Characteristic classes of oriented six-dimensional submanifolds in the octonions,” Kodai Math. J., 16, 65–73 (1993).

  81. 81.

    H. Hashimoto, “Oriented six-dimensional submanifolds in the octonions,” Int. J. Math. Math. Sci., 18, 111–120 (1995).

  82. 82.

    H. Hashimoto, T. Koda, K. Mashimo, and K. Sekigawa, “Extrinsic homogeneous Hermitian six-dimensional submanifolds in the octonions,” Kodai Math. J., 30, 297–321 (2007).

  83. 83.

    Z. Hu and Y. Zhang, “Rigidity of the almost complex surfaces in the nearly K¨ahlerian S3×S3,” J. Geom. Phys., 100, 80–91 (2016).

  84. 84.

    N. E. Hurt, Geometric Quantization in Action. Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory, Reidel, Dordrecht–Boston–London (1983).

  85. 85.

    S. Ianus, Geometrie diferentială cu aplicaţii în teoria relativităţii, Editura Acad. Române, Bucureşti (1983).

  86. 86.

    Y. Ishii, “On conharmonic transformations,” Tensor, N.S., 7, 73–80 (1957).

  87. 87.

    J. Jost, Riemannian Geometry and Geometric Analysis, Springer-Verlag, Berlin–Heidelberg–New-York (2003).

  88. 88.

    A. L. Kholodenko, Applications of Contact Geometry and Topology in Physics, World Scientific, New Jersey–London–Singapore (2013).

  89. 89.

    H. S. Kim and R. Takagi, “The type number of real hypersurfaces in Pn(C),” Tsukuba J. Math., 20, 349–356 (1996).

  90. 90.

    V. F. Kirichenko, “Almost Kählerian structures indiced by 3”=vector products on sixdimensional submanifolds of the Cayley algebra,” Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., 3, 70–75 (1973).

  91. 91.

    V. F. Kirichenko, “Classification of Kählerian structures induced by 3”=vector products on sixdimensional submanifolds of the Cayley algebra,” Izv. Vyssh. Ucheb. Zaved. Ser. Mat., No. 8, 32–38 (1980).

  92. 92.

    V. F. Kirichenko, “Stability of almost Hermitian structures induced by 3”=vector products on six-dimensional submanifolds of the Cayley algebra,” Ukr. Geom. Sb., 25, 60–68 (1982).

  93. 93.

    V. F. Kirichenko, “Methods of generalized Hermitian geometry in the theory of almost contact manifolds,” Itogi Nauki Tekh. Probl. Geom., 18, 25–71 (1986).

  94. 94.

    V. F. Kirichenko, Differential-Geometric Structures on Manifolds [in Russian], Odessa (2013).

  95. 95.

    V. F. Kirichenko and M. B. Banaru, “Almost contact metric structures on hypersurfaces of almost Hermitian manifolds,” Itogi Nauki Tekh. Sovr. Mat. Prilozh. Temat. Obzory, 127, 5–40 (2014).

  96. 96.

    V. F. Kirichenko, A. R. Rustanov, and A. Shikhab, “Geometry of the tensor of conharmonic curvature of an almost Hermitian manifold,” Mat. Zametki, 90, No. 1, 87–103 (2011).

  97. 97.

    V. F. Kirichenko and A. A. Shihab, “On the geometry of conharmonic curvature tensor for nearly Kählerian manifolds,” Fundam. Prikl. Mat., 16, No. 2, 43–54 (2010).

  98. 98.

    V. F. Kirichenko and I. V. Uskorev, “Invariants of conformal transformations of almost contact metric structures,” Mat. Zametki, 84, No. 6, 838–850 (2008).

  99. 99.

    V. F. Kirichenko and L. I. Vlasova, “Concircular geometry of nearly Kählerian manifolds,” Mat. Sb., 193, No. 5, 51–76 (2002).

  100. 100.

    Sh. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I, Interscience, New York–London (1963).

  101. 101.

    Sh. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II, Interscience, New York–London (1969).

  102. 102.

    H. Kurihara, “On real hypersurfaces in a complex space form,” Math. J. Okayama Univ., 40, 177–186 (1998).

  103. 103.

    H. Kurihara, “The type number on real hypersurfaces in a quaternionic space form,” Tsukuba J. Math., 24, 127–132 (2000).

  104. 104.

    H. Kurihara and R. Takagi, “A note on the type number of real hypersurfaces in Pn(C),” Tsukuba J. Math., 22, 793–802 (1998).

  105. 105.

    E. V. Kusova, On Geometry of Weakly Cosymplectic Structures [in Russian], Ph.D. thesis, Moscow (2013).

  106. 106.

    M. Matsumoto, “On six-dimensional almost Tachibana spaces,” Tensor, N.S., 23, 250–252 (1972).

  107. 107.

    A. S. Mishchenko and A. T. Fomenko, A Course of Differential Geometry and Topology [in Russian], Moscow (1980).

  108. 108.

    A. Moroianu and U. Semmelmann, “Infinitesimal Einstein deformations of nearly Kählerian metrics,” Trans. Am. Math. Soc., 363, No. 6, 3057–3069 (2011).

  109. 109.

    P.-A. Nagy, “On nearly-Kählerian geometry,” Ann. Global Anal. Geom., 22, 167–178 (2002).

  110. 110.

    R. Nivas and A. Agnihotri, “On semisymmetric nonmetric connections on a nearly Kählerian manifold,” Tensor, N.S., 72, 279–284 (2010).

  111. 111.

    E. Omachi, “On nearly K¨ahlerian manifolds with almost analytic Ricci operator,” Tensor, N.S., 71, 87–90 (2009).

  112. 112.

    G. Pitiş, Geometry of Kenmotsu Manifolds, Publ. House Transilvania Univ., Braşov (2007).

  113. 113.

    P. K. Rashevskii, Riemannian Geometry and Tensor Analysis [in Russian], Nauka, Moscow (1967).

  114. 114.

    K. Sekigawa, “Almost complex submanifolds of a six-dimensional sphere,” Kodai Math. J., 6, 174–185 (1983).

  115. 115.

    R. Sharma and S. Deshmukh, “On Lagrangian submanifolds of the nearly Kählerian 6-sphere,” Contemp. Math., 674, 153–160 (2016).

  116. 116.

    S. S. Shern, M. P. Do Carmo, and Sh. Kobayashi, “Minimal submanifolds of a sphere with second fundamental form of constant length,” in: Functional Analysis and Related Fields, Springer-Verlag, Berlin (1970), pp. 59–75.

  117. 117.

    L. V. Stepanova, “Quasi-Sasakian structures on hypersurfaces of Hermitian manifolds,” Nauch. Tr. Mosk. Ped. Gos. Univ., 187–191(1995).

  118. 118.

    L. V. Stepanova, Quasi-Sasakian structures on hypersurfaces of Hermitian manifolds [in Russian], Ph.D. thesis, Moscow (1995).

  119. 119.

    L. V. Stepanova, G. A. Banaru, and M. B. Banaru, “On quasi-Sasakian hypersurfaces of Kählerian manifolds,” Izv. Vyssh. Ucheb. Zaved. Ser. Mat., No. 1, 86–89 (2016).

  120. 120.

    R. Takagi, “A class of hypersurfaces with constant principal curvatures in a sphere,” J. Differ. Geom., 11, 225–233 (1976).

  121. 121.

    F. Tricerri and L. Vanhecke, “Curvature tensors on almost Hermitian manifolds,” Trans. Am. Math. Soc., 267, 365–398 (1981).

  122. 122.

    L. Vanhecke, “The Bochner curvature tensor on almost Hermitian manifolds,” Geom. Dedicata, 6, 389–397 (1977).

  123. 123.

    L. Vezzoni, “On the canonical Hermitian connection in nearly Kähler manifolds,” Kodai Math. J., 32, 420–431 (2009).

  124. 124.

    L. Vranchen, “Special Lagrangian submanifolds of the nearly Kähler 6-sphere,” Glasgow Math. J., 45, 415–426 (2003).

  125. 125.

    K. Yano, Differential Geometry on Complex and Almost Complex Spaces, Pergamon Press, Oxford (1965).

  126. 126.

    K. Yano and S. Ishihara, “Almost contact structures induced on hypersurfaces in complex and almost complex spaces,” Kodai Math. Sem. Rep., 17, No. 3, 222–249 (1965).

  127. 127.

    K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore (1984).

Download references

Author information

Correspondence to M. B. Banaru.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 146, Geometry, 2018.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Banaru, M.B. On the Six-dimensional Sphere with a Nearly Kählerian Structure. J Math Sci 245, 553–567 (2020). https://doi.org/10.1007/s10958-020-04711-6

Download citation

Keywords and phrases

  • ordinary differential equation
  • invariant
  • connection
  • classification
  • differential-algebraic characteristics
  • symmetry group

AMS Subject Classification

  • 34A26
  • 53A55