Generic Submersions from Kaehler Manifolds

  • Cem SayarEmail author
  • Hakan Mete Taṣtan
  • Fatma Özdemir
  • Mukut Mani Tripathi


In the present paper, we introduce a new kind of Riemannian submersion such that the fibers of such submersion are generic submanifolds in the sense of Ronsse that we call generic submersion. Some examples are given for generic submersion. Necessary and sufficient conditions are found for the integrability and totally geodesicness of the distributions which are mentioned in the definition. The geometry of the fibers is investigated. New results are obtained by considering the parallelism condition of canonical structures.


Riemannian submersion Generic submersion Skew CR-submersion Horizontal distribution Kaehlerian manifold 

Mathematics Subject Classification

53C15 53B20 



  1. 1.
    Ali, S., Fatima, T.: Generic Riemannian submersions. Tamkang J. Math. 44(4), 395–409 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Akyol, M.A.: Generic Riemannian submersions from almost product Riemannian manifolds. GUJ Sci. 30(3), 89–100 (2017)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Akyol, M.A.: Conformal semi-slant submersions. Int. J. Geom. Methods Mod. Phys. 14(7), 1750114 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, B.Y.: Differential geometry of real submanifolds in a Kaehler manifold. Monatsh Math. 91, 257–274 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Chen, B.Y., Garay, O.: Pointwise slant submanifolds in almost Hermitian manifolds. Turk. J. Math. 364, 630–640 (2012)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Erken, İKüpeli, Murathan, C.: On slant submersions for cosymplectic manifolds. Bull. Korean Math. Soc. 51(66), 1749–1771 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Etayo, F.: On quasi-slant submanifolds of an almost Hermitian manifold. Publ. Math. Debr. 53(1–2), 217–223 (1998)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Falcitelli, M., Ianus, S., Pastore, A.M.: Riemannian Submersions and Related Topics. World Scientific, River Edge (2004)CrossRefzbMATHGoogle Scholar
  9. 9.
    Gray, A.: Pseudo-Riemannian almost product manifolds and submersion. J. Math. Mech. 16, 715–737 (1967)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Gündüzalp, Y.: Anti-invariant Riemannian submersions from almost product Riemannnian manifolds. Math. Sci. Appl. E Notes 1, 58–66 (2013)zbMATHGoogle Scholar
  11. 11.
    Lee, J.W., Ṣahin, B.: Pointwise slant submersions. Bull. Korean Math. Soc. 51, 1115–1126 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    O’Neill, B.: The fundamental equations of a submersion. Mich. Math. J. 13, 458–469 (1966)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Özdemir, F., Sayar, C., Taṣtan, H.M.: Semi-invariant submersions whose total manifolds are locally product Riemannian. Quaest. Math. 40(7), 909–926 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Park, K.S., Prasad, R.: Semi-slant submersions. Bull. Korean Math. Soc. 50(3), 951–962 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Ronsse, G.B.: Generic and skew CR-submanifolds of a Kaehler manifold. Bull. Inst. Math. Acad. Sin. 18, 127–141 (1990)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Ṣahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Cent. Eur. J. Math. 8(3), 437–447 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Ṣahin, B.: Slant submersions from almost Hermitian manifolds. Bull. Math. Soc. Sci. Math. Roum. 54 (102)(1), 93–105 (2011)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Ṣahin, B.: Semi-invariant submersions from almost Hermitian manifolds. Can. Math. Bull. 56(1), 173–182 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Ṣahin, B.: Riemannian Submersions, Riemannian Maps in Hermitian Geometry and Their Applications. Elsevier, Academic Press, Cambridge (2017)zbMATHGoogle Scholar
  20. 20.
    Aykurt, S.A., Ergüt, M.: Pointwise slant submersions from cosymplectic manifolds. Turk. J. Math. 40(3), 582–593 (2016)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Taştan, H.M.: On Lagrangian submersions. Hacet. J. Math. Stat. 43(6), 993–1000 (2014)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Taştan, H.M., Ṣahin, B.: Ṣ, Yanan, Hemi-slant submersions. Mediterr. J. Math. 13(4), 2171–2184 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Taştan, H.M., Özdemir, F., Sayar, C.: On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian. J. Geom. 108, 411–422 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Tripathi, M.M.: Generic submanifolds of generalized complex space forms. Publ. Math. Debr. 503–4, 373–392 (1997)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Watson, B.: Almost Hermitian submersions. J. Differ. Geom. 11(1), 147–165 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Vilms, J.: Totally geodesic maps. J. Differ. Geom. 4, 73–79 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Yano, K., Kon, M.: Structures on Manifolds. World Scientific, Singapore (1984)zbMATHGoogle Scholar
  28. 28.
    Yano, K., Kon, M.: Generic submanifolds. Ann. Mat. 123, 59–92 (1980)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  • Cem Sayar
    • 1
    Email author
  • Hakan Mete Taṣtan
    • 2
  • Fatma Özdemir
    • 1
  • Mukut Mani Tripathi
    • 3
  1. 1.Department of Mathematics, Faculty of Science and LettersIstanbul Technical UniversityIstanbulTurkey
  2. 2.Department of MathematicsIstanbul UniversityIstanbulTurkey
  3. 3.DST-CIMS, Department of Mathematics, Faculty of Science and LettersBanaras Hindu UniversityVaranasiIndia

Personalised recommendations