Abstract
We prove that an almost contact metric structure on an orientable hypersurface with type number 1 in a Kählerian manifold is necessarily cosymplectic.
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References
Gray A. and Hervella L. M., “The sixteen classes of almost Hermitian manifolds and their linear invariants,” Ann. Mat. Pura Appl., 123,No. 4, 35–58 (1980).
Blair D. E., Contact Manifolds in Riemannian Geometry, Springer-Verlag, Heidelberg, Berlin, and New York (1976) (Lectures Notes in Math.; 509).
Stepanova L. V., “Quasi-Sasakian structure on hypersurfaces in Hermitian manifolds,” Nauch. Tr. MPGU im. V. I. Lenina, 187–191 (1995).
Stepanova L. V. and Banaru M. B., “On hypersurfaces of quasi-Kählerian manifolds,” An. Stiint. Univ. Al. I. Cuza Iasi, 47,No. 1, 65–70 (2001).
Banaru M., “On minimality of a Sasakian hypersurface in a W3-manifold,” Saitama Math. J., 20, 1–7 (2002).
Banaru M. B., “On the Kenmotsu hypersurfaces of special Hermitian manifolds,” Siberian Math. J., 45,No. 1, 7–10 (2004).
Kirichenko V. F., Differential Geometric Structures on Manifolds [in Russian], Pechatnyĭ Dom, Odessa (2013).
Blair D. E., Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston, Basel, and Berlin (2002).
Kiritchenko V. F., “Sur la gèomètrie des variètès approximativement cosymplectiques,” C. R. Acad. Sci. Paris Ser. 1, 295,No. 12, 673–676 (1982).
Sasaki S., “On differentiable manifolds with certain structures which are closely related to almost contact structures,” Tohoku Math. J., 12,No. 3, 459–476 (1960).
Kurihara H., “The type number on real hypersurfaces in a quaternionic space form,” Tsukuba J. Math., 24, 127–132 (2000).
Banaru M. B., “On Sasakian hypersurfaces in 6-dimensional Hermitian submanifolds of the Cayley algebra,” Sb. Math., 194,No. 8, 1125–1136 (2003).
Abu-Saleem A. and Banaru M., “Some applications of Kirichenko tensors,” An. Univ. Oradea Fasc. Mat., 17,No. 2, 201–208 (2010).
Banaru M., “On the Gray-Hervella classes of AH-structures on six-dimensional submanifolds of Cayley algebra,” Ann. Univ. Sofia “St. Kl. Ohridski” Math., 95, 125–131 (2004).
Banaru M. B., “On cosymplectic hypersurfaces of six-dimensional Kählerian submanifolds of the Cayley algebra,” Russian Math. (Iz. VUZ), 47,No. 7, 60–63 (2003).
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Original Russian Text Copyright © 2014 Banaru M.B.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 4, pp. 719–723, July–August, 2014.
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Banaru, M.B. On almost contact metric 1-hypersurfaces in Kählerian manifolds. Sib Math J 55, 585–588 (2014). https://doi.org/10.1134/S0037446614040016
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DOI: https://doi.org/10.1134/S0037446614040016