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arXiv · 1605.05592

Bach-flat noncompact steady quasi-Einstein manifolds

M. Ranieri·E. Ribeiro Jr
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Abstract

The goal of this article is to study the geometry of Bach-flat noncompact steady quasi-Einstein manifolds. We show that a Bach-flat noncompact steady quasi-Einstein manifold $(M^{n},\,g)$ with positive Ricci curvature such that its potential function has at least one critical point must be a warped product with Einstein fiber. In addition, the fiber has constant curvature if $n = 4.$

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M. Ranieri, E. Ribeiro Jr. 2016-12-14. Bach-flat noncompact steady quasi-Einstein manifolds. https://arxiv.org/abs/1605.05592

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