On Warped Product Super Generalized Recurrent Manifolds

Received: 30.X.2015, Accepted: 16.II.2016

Abstract. The object of the present paper is to obtain the characterization of a warped product semi-Riemannian manifold with a special type of recurrent like structure, called super generalized recurrent. As consequence of this result we also find out the necessary and sufficient conditions for a warped product manifold to satisfy some other recurrent like structures such as weakly generalized recurrent manifold, hyper generalized recurrent manifold etc. Finally as a support of the main result, we present an example of warped product super generalized recurrent manifold.

Keywords: Recurrent manifold, weakly generalized recurrent manifold, hyper generalized recurrent manifold, super generalized recurrent manifold, warped product manifold

Mathematics Subject Classification (2010): 53C15, 53C25, 53C35

Authors:
Absos Ali Shaikh, Department of Mathematics, The University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India
Haradhan Kundu, Department of Mathematics, The University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India
Md. Showkat Ali, Department of Mathematics, Dhaka University, Dhaka-1000, Bangladesh