On warped product manifolds satisfying some pseudosymmetric type conditions

Abstract

The object of the present paper is to study the characterization of warped product manifolds satisfying some pseudosymmetric type conditions, especially, due to projective curvature tensor. For this purpose we consider a warped product manifold satisfying the pseudosymmetric type condition $R\cdot R=L_{1}Q(g,R)+L_{2}Q(S,R)$ and evaluate its characterization theorem. As special cases of $L_1$ and $L_2$ we find out the necessary and sufficient condition for a warped product manifold to satisfy various pseudosymmetric type, such as pseudosymmetry, Ricci generalized pseudosymmetry, semisymmetry due to projective curvature tensor ($P\cdot R=0$), pseudosymmetry due to projective curvature tensor ($P\cdot R=LQ(g,R)$) etc. Finally we present some suitable examples of warped product manifolds satisfying such pseudosymmetric type conditions.

Paper contains 17 pages, a table, 6 theorems and 13 corollaries

References in corpus (6)

• On pseudosymmetric manifolds
• Natural Intrinsic Geometrical Symmetries
• On generalized Roter type manifolds
• On Warped Product Super Generalized Recurrent Manifolds
• On warped product generalized Roter type manifold
• On some curvature restricted geometric structures for projective curvature tensor

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