On Bach flat warped product Einstein manifolds

Qiang Chen; Chenxu He

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arXiv · 1105.3957

On Bach flat warped product Einstein manifolds

Qiang Chen·Chenxu He

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Abstract

In this paper we show that a compact warped product Einstein manifold with vanishing Bach tensor of dimension $n \geq 4$ is a finite quotient of a warped product with $(n-1)$-dimensional Einstein fiber. The fiber has constant curvature if $n=4$.

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Qiang Chen, Chenxu He. 2011-05-19. On Bach flat warped product Einstein manifolds. https://arxiv.org/abs/1105.3957

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