On Generalized Phi-Recurrent Kenmotsu Manifolds

Abstract

The aim of the present paper is to study the properties of generalized ϕ−recurrent and concircular ϕ−recurrent Kenmotsu manifolds

Keywords

• Generalized ϕ−recurrent, generalized concircular ϕ−recurrent, η−Einstein and Kenmotsu manifolds.

References

1. Sasaki, S., (1965, 1967, 1968), Almost contact manifolds, I, II, III, A Lecture note, Tohoku University.
2. Takahashi, T., (1977), Sasakian ϕ−symmetric spaces, Tohoku Math. J., 29, pp. 91-113.
3. De, U. C. and Pathak, G., (2004), On 3−dimensional Kenmotsu manifolds, Indian J. pure Appl. Math., 35, pp. 159-165.
4. Kenmotsu, K., (1972), A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, pp. 103.
5. De, U. C. and Guha, N., (1991) , On generalized recurrent manifolds, Proceedings of the Mathematical Society, 7, pp. 7-11.
6. Chen, B. Y., (1973), Geometry of submanifolds, M. Dekker Inc., New York.
7. Yano, K., (1944), On the torseforming direction in Riemannian spaces, Proc. Imp. Acad. Tokyo, 20, pp. 340-345.
8. Chaubey, S. K., (2013), On generalized ϕ−recurrent trans-Sasakian manifolds, (to appear).

9. Patil, D. A., Prakasha, D. G. and Bagewadi, C. S., (2009), On generalized ϕ−recurrent Sasakian manifolds, Bull. of Math. Anal. and Appl., 1 (3), pp. 42-48.
10. Jaiswal, J. P. and Ojha, R. H., (2009) , On generalized ϕ−recurrent LP-Sasakian manifolds, Kyung- pook Math. J., 49, pp. 779-788.
11. Venkatesha and Bagewadi, C. S., (2005), On 3−dimensional trans-Sasakian manifolds, AMSE, 42(5), pp. 63-73.
12. Kobayashi, K. and Nomizu, K., (1963), Foundations of Differential Geometry, I, II, Wiley-Interscience, New York.
13. Sinha, B. B. and Srivastava, A. K., (1991), Curvatures on Kenmotsu manifold, Indian J. Pure Appl. Math., 22, (1), pp. 23-28.
14. Jun, J. B., De, U. C. and Pathak, G., (2005), On Kenmotsu manifolds, J. Korean Math. Soc., 42, pp. 445.
15. De, U. C., Yildiz, A. and Yaliniz, Funda, (2008), On ϕ−recurrent Kenmotsu manifolds, Turk J. Math., , pp. 1-12.
16. Sasaki, S. and Hatakeyama, Y., (1961), On differentiable manifolds with certain structures which are closely related to almost contact structure, Tohoku Math. J., 13, pp. 281-294.
17. Chaubey, S. K. and Ojha, R. H., (2010), On m-projective curvature tensor of a Kenmotsu manifold, Diff. Geom. Dyn. Sys., 12, pp. 52-60.
18. De, U. C., (2008), On ϕ−symmetric Kenmotsu manifolds, International Electronic J. of Geom., 1 (1), pp. 33-38.
19. Cihan, ¨O . and De, U. C., (2006), On the quasi-conformal curvature tensor of a Kenmotsu manifolds
20. Mathematica Pannonica, 17/2, pp. 221-228. Basari, A. and Murathan, C., (2008), On generalized ϕ−recurrent Kenmotsu manifolds, Fen Derg. (1), pp. 91-97.
21. De, U. C. and Guha, N., (1991), On generalized recurrent manifolds, J. Nat. Acad. Math. India, 9, pp. 85-92.
22. Cihan, ¨O ., (2007), On generalized recurrent Kenmotsu manifolds, Word Applied Sci. J., 2(1), pp. 33.