On Bach flat warped product Einstein manifolds

By Qiang Chen, Chenxu He. 2011

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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 $n=4$.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2a3d3b4363917c2118ff1cbdf9f175c6fc98ba78