Bach-flat noncompact steady quasi-Einstein manifolds
M. Ranieri, E. Ribeiro Jr

TL;DR
This paper investigates the geometric structure of Bach-flat noncompact steady quasi-Einstein manifolds, revealing conditions under which they form warped products with Einstein fibers, especially in four dimensions.
Contribution
It establishes that such manifolds with positive Ricci curvature and a critical point in the potential function are warped products with Einstein fibers, with special results in four dimensions.
Findings
Manifolds are warped products with Einstein fibers.
Fiber has constant curvature when dimension is four.
Conditions relate Bach-flatness, steady quasi-Einstein, and positive Ricci curvature.
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 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
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Black Holes and Theoretical Physics
