Bach-flat noncompact steady quasi-Einstein manifolds

2016/05/18 by M. Ranieri, Ranieri, M., E. Ribeiro +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1605.05592

openalex publication_date 2016/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (Mⁿ, 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.

Citations

• A note on static spaces and related problems

Related

• On Bach flat warped product Einstein manifolds
• On the classification of noncompact steady quasi-Einstein manifold with vanishing condition on the Weyl tensor
• Rigidity theorem for compact Bach-flat manifolds with positive constant σ₂
• Quasi-Einstein manifolds with structure of warped product product
• Remarks on potential functions of noncompact quasi-Einstein manifolds