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Bach-flat noncompact steady quasi-Einstein manifolds

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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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Correspondence to E. Ribeiro Jr..

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E. Ribeiro was partially supported by CNPq/Brazil, M. Ranieri was partially supported by CAPES/Brazil.

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Ranieri, M., Ribeiro, E. Bach-flat noncompact steady quasi-Einstein manifolds. Arch. Math. 108, 507–519 (2017). https://doi.org/10.1007/s00013-016-1014-z

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