On warped product generalized Roter type manifold

Abstract

Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci tensors upto level 2. The object of the present paper is to investigate the characterizations of a warped product manifold to be generalized Roter-type. We also present an example of a warped product manifold which is generalized Roter type but not Roter type, and also an example of a warped product manifold which is Roter type but not conformally flat. These examples ensure the proper existence of such notions.

16 pages

References in corpus (2)

• On pseudosymmetric manifolds
• Curvature properties of interior black hole metric

Cited by in corpus (9)

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• On generalized Roter type manifolds
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• On warped product manifolds satisfying some pseudosymmetric type conditions
• Curvature properties of Vaidya metric
• On some curvature restricted geometric structures for projective curvature tensor
• Curvature properties of interior black hole metric
• Curvature properties of generalized pp-wave metric
• Curvature properties of Robinson-Trautman metric