Document Type
Article
Date
1-24-2011
Disciplines
Mathematics
Description/Abstract
In this paper we take the perspective introduced by Case-Shu-Wei of studying warped product Einstein metrics through the equation for the Ricci curvature of the base space. They call this equation on the base the m-Quasi Einstein equation, but we will also call it the (lambda,n+m)-Einstein equation. In this paper we extend the work of Case-Shu-Wei and some earlier work of Kim-Kim to allow the base to have non-empty boundary. This is a natural case to consider since a manifold without boundary often occurs as a warped product over a manifold with boundary, and in this case we get some interesting new canonical examples. We also derive some new formulas involving curvatures which are analogous to those for the gradient Ricci solitons. As an application, we characterize warped product Einstein metrics when the base is locally conformally flat.
Recommended Citation
He, Chenxu; Petersen, Peter; and Wylie, William, "On the Classification of Warped Product Einstein Metrics" (2011). Mathematics - All Scholarship. 130.
https://surface.syr.edu/mat/130
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This article is from arXiv.org, for more information see http://arxiv.org/abs/1010.5488