Characterizations Of Weakly Conformally Flat And Quasi Einstein Manifolds

Ramesh Sharma

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arXiv · 2212.00559

Characterizations Of Weakly Conformally Flat And Quasi Einstein Manifolds

Ramesh Sharma

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Abstract

First, we show that a warped product of a line and a fiber manifold is weakly conformally flat and quasi Einstein if and only if the fiber is Einstein. Next, we characterize and classify contact (in particular, $K$-contact) Riemannian manifold satisfying weakly (and doubly weakly) conformally flat and quasi-Einstein ($\eta$-Einstein) conditions. Finally, we provide local classification and characterization of a semi-Riemannian (including the 4-dimensional spacetime) with harmonic Weyl tensor and a non-homothetic conformal (including closed) vector field, in terms of Petrov types and Bach tensor.

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Ramesh Sharma. 2022-12-01. Characterizations Of Weakly Conformally Flat And Quasi Einstein Manifolds. https://arxiv.org/abs/2212.00559

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