On Contact CR-Submanifolds of a Kenmotsu Manifold

Abstract

In this paper, we study the dierential geometry of contact CR-submanifolds of a Kenmotsu manifold.

Necessary and sucient conditions are given for a submanifold to be a contact CR-submanifold in Kenmotsu

manifolds. Finally, the induced structures on submanifolds are investigated, these structures are categorized and we

discuss these results

Keywords

• kenmotsu manifold,contact cr submanifold

References

1. Arslan, K., Ezentas, R., Mihai, I., Murathan, C., Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42(5)(2005), 1101-1110. 1
2. Atçeken, M., Contact CR-warped product submanifolds in cosymplectic space forms, Collect. Math., (2011), 62:1726 DOI 10.1007/s13348- 010-0002-z. 1
3. Atçeken, M., Contact CR-warped product submanifolds in cosymplectic manifolds, Kyungpook Math. J., 56(2016), 965-977. 1
4. Atçeken, M., Contact CR-submanifolds of Kenmotsu manifolds, Serdica Math. J., 37(2011), 67-78. 1
5. Atçeken, M., Dirik, S., Contact CR-submanifolds of Kenmotsu manifolds, Acta Univ. Sapientiae, Mathematica, 4(2)(2012), 182-198. 1, 3.2
6. Bejancu, A., Geometry of CR-submanifolds, Kluwer, Dortrecht (1986). 1
7. Bejancu, A., CR-submanifolds of a Kaehler manifold, Proc. Amer. Math. Soc., 69 (1978), 135-142. 1
8. Blair, D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Vol. 509. Springer-Verlag, New York, (1976). 1

9. Blair, D. E., Chen, B.Y., On CR-submanifolds of Hermitian manifold, Israel Journal of Mathematics, 34 (1980), 353-363.
10. Dirik, S., On Contact CR-Submanifolds of a Cosymplectic Manifold, Filomat, 32 (14)(2018), In press. 3.10
11. Hasegawa, I., Mihai, I,. Contact CR-warped product submanifolds in Sasakian Manifolds, Geom. Dedicata, 102(2003), 143-150.
12. Hui, S. K., Mandal, P., Pseudo parallel contact CR-submanifolds of Kenmotsu manifolds, Indian Journal of Mathematics, 59(3)(2017), 385-402.
13. Kenmotsu, K., A Class of almost contact Riemannian manifold. Tohoku Math. J. 24 (1972), 93-103.
14. Matsumato, K., Contact CR-submanifolds of Sasakian manifolds, Internat. J. Math., 6(2)(1983), 303-326.
15. Uddin, S., Khan, K. A., Warped product CR-submanifolds of cosymplectic manifolds, Ricerche di Matematica, 60(1)(2011), 143-149.
16. Uddin, S., Khan, V. A., Khan, K. A., A note on warped product submanifolds of Cosymplectic manifolds, Filomat, 24(3)(2010), 95-102.