Special CR maximal dimensional submanifolds in the Kenmotsu space forms

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Basic Since, Azarbaijan Shahid Madani University, Tabriz, Iran

Abstract

The (n +1)-dimensional almost metric contact submanifolds wuth maximal CR- submanifolds of (n-1) in the Kenmotsu space forms classified such that n > 5 and h(FX, Y )-h(X, FY )= g(FX,Y)ζ for vector fields X, Y tangent to M, where h and F denote the second fundamental form and a skew-symmetric endomorphism acting on the tangent space of M, respectively, and ζ a non zero normal vector field to M.

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References

1. A. Bejancu, CR-submanifolds of Kaeher Manifold I, Proc. Amer. Math. Soc. 69(1978),135-142.
2. A. Bejancu, Geometry of CR-submanifolds, D. Reidel Publishing Company, Dordrecht,Boston, Lancaster, Tokyo, 1986.
3. D. E. Blair,, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics,Vol. 509, Springer-Verlag, Berlin, 1976.
4. M. Djoric and M. Okumura, Certain CR submanifolds of maximal CR dimension of complex space forms, Diff. Geom. and App. 26(2008), 208-217.
5. M. Djoric and M. Okumura, CR Submanifolds of Complex Projective Space, Developments in Mathematics, Vol. 19, Springer-Verlag, New York, 2010.
6. M. Ilmakchi, CR Maximal Dimensional Submanifolds of Kenmotsu Space Forms, Vietnam J. Math., 50(2022), 171–181.
7. M. Ilmakchi and E. Abedi, Contact CR Submanifolds of maximal contact CR dimension of Sasakian Space Form,Mathematical Researches (Sci. Kharazmi University), 6(2020),1-12.
8. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J.24(1972), 93-103.
9. H. S. Kim, D. K. Choi and J. S. Pak, Certain class of contact CR-submanifolds of a Sasakian space form, Commun. Korean Math. Soc. 29(2014), 131-140.
10. H. S. Kim and J. S. Pak, Certain contact CR-submanifolds of an odd-dimensional unit sphere, Bull. Korean Math. Soc. 44(2007), 109-116.
11. H. S. Kim and J. S. Pak, Certain class of contact CR-submanifolds of an odd-dimensional unit sphere, Taiwanese J. Math. 14(2010), 629-646.
12. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry I, Wiley and Sons Inc. New York-London, 1963.
13. K. Yano and M. Kon, Structure on Manifold, World Scientific, Singapore, 1984.
Journal of Finsler Geometry and its Applications
Volume 5, Issue 2
December 2024
Pages 127-142

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