On some class of warped product manifolds

The symmetry of warped product space-times

In the literature we see that after introducing a geometric structure by imposing some restrictions on Riemann–Christoffel curvature tensor, the same type structures given by imposing same restriction on other curvature tensors being studied. The main object of the present paper is to study the equivalency of various geometric structures obtained by same restriction imposing on different curvature tensors. In this purpose we present a tensor by combining Riemann–Christoffel curvature tensor, Ricci tensor, the metric tensor and scalar curvature which describe various curvature tensors as its particular cases. Then with the help of this generalized tensor and using algebraic classification we prove the equivalency of different geometric structures (see Theorems 6.3, 6.4, 6.5, 6.6 and 6.7; Tables 1 and 2).

On equivalency of various geometric structures

We investigate semi-Riemannian manifolds satisfying some curva- ture conditions. Those conditions are strongly related to pseudosymmetry.

/pdf/on-riemann-and-weyl-compatible-tensors-3eggest7fd.pdf

On Riemann and Weyl Compatible Tensors

A proposal is made for what could well be the most natural symmetrical Rie- mannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or, still, the spaces which satisfy the axiom of free mobility.

/pdf/natural-intrinsic-geometrical-symmetries-2unwilpw2i.pdf

Natural Intrinsic Geometrical Symmetries

/pdf/on-four-dimensional-riemannian-warped-product-manifolds-39fevfbmtt.pdf

On some class of warped product manifolds

Citations

The symmetry of warped product space-times

On equivalency of various geometric structures

On Riemann and Weyl Compatible Tensors

Natural Intrinsic Geometrical Symmetries

On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions

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