Einstein-type manifolds with complete divergence of Weyl and Riemann tensor
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In this paper, we study Einstein-type manifolds generalizing static spaces and $V$-static spaces. We prove that if an Einstein-type manifold has non-positive complete divergence of its Weyl tensor and non-negative complete divergence of Bach tensor, then $M$ has harmonic Weyl curvature. Also similar results on an Einstein-type manifold with complete divergence of Riemann tensor are proved.
Abstract
In this paper, we study Einstein-type manifolds generalizing static spaces and $V$-static spaces. We prove that if an Einstein-type manifold has non-positive complete divergence of its Weyl tensor and non-negative complete divergence of Bach tensor, then $M$ has harmonic Weyl curvature. Also similar results on an Einstein-type manifold with complete divergence of Riemann tensor are proved.
참고문헌 (8)
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