On a Class of P-Kenmotsu Manifolds Admitting Weyl-projective Curvature Tensor of Type (1, 3)

K. L. Sai Prasad^1, , S. Sunitha Devi² and G. V. S. R. Deekshitulu³

¹Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Visakhapatnam, India

²Department of Mathematics, Vignan Institute of Information Technology, Visakhapatnam, India

³Department of Mathematics, Jawaharlal Nehru Technological University, Kakinada, India

Cite this paper:
K. L. Sai Prasad, S. Sunitha Devi and G. V. S. R. Deekshitulu. On a Class of P-Kenmotsu Manifolds Admitting Weyl-projective Curvature Tensor of Type (1, 3). Turkish Journal of Analysis and Number Theory. 2018; 6(6):155-158. doi: 10.12691/tjant-6-6-2

Abstract

We study a class of para-Kenmotsu manifolds admitting Weyl-projective curvature tensor of type (1, 3). At the end, it is shown that an n-dimensional (n > 2) P-Kenmotsu manifold is Ricci semisymmetric if and only if it is an Einstein manifold.

Keywords:
para kenmotsu manifold recurrent manifold W₂ - Curvatute tensor ricci tensor einstein manifold

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References:

[1]	Sato, I, On a structure similar to the almost contact structure, Tensor (N.S.), 30, 219-224, 1976.
[2]	Sato, I, On a structure similar to the almost contact structure II, Tensor (N.S.), 31, 199-205, 1977.
[3]	Adati, T. and Matsumoto, K, On conformally recurrent and conformally symmetric P-Sasakian Manifolds, TRU Math., 13, 25-32, 1977.
[4]	Adati, T. and Miyazawa, T, On P-Sasakian manifolds admitting some parallel and recurrent tensors, Tensor (N.S.), 33, 287-292, 1979.
[5]	De, U. C. and Avijit Sarkar, On a type of P-Sasakian manifolds, Math. Reports, 11(2), 139-144, 2009.
[6]	Matsumoto, K., Ianus, S. and Ion Mihai, On P-Saskian manifolds which admit certain tensor fields, Publ. Math. Debrecen, 33, 61-65, 1986.
[7]	Kenmotsu, K, A class of almost contact Riemannian manifolds, Tohoku Math. Journal, 24, 93-103, 1972.
[8]	Sinha, B. B. and Sai Prasad, K. L, A class of almost para contact metric Manifold, Bulletin of the Calcutta Math. Soc., 87, 307-312, 1995.
[9]	Pokhariyal, G. P. and Mishra, R. S, The curvature tensors and their relativistic significance, Yokohoma Math. J., 18, 105-108, 1970.
[10]	Pokharial, G. P, Study of a new curvature tensor in a Sasakian manifold, Tensor (N.S.), 36, 222-225, 1982.
[11]	Sai Prasad, K. L. and Satyanarayana, T, Some curvature properties on a Special paracontact Kenmotsu manifold with respect to Semi-symmetric connection, Turkish Journal of Analysis and Number Theory, 3(4), 94-96, 2015.