Document Type
Article
Date
12-15-2010
Disciplines
Mathematics
Description/Abstract
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the base is three dimensional and the dimension of the fiber is greater than one we show that the space is always rigid. We also exhibit examples of solvable four dimensional Lie groups that can be used as the base space of non-rigid warped product Einstein metrics showing that the result is not true in dimension greater than three. We also give some further natural curvature conditions that characterize the rigid examples in higher dimensions.
Recommended Citation
He, Chenxu; Petersen, Peter; and Wylie, William, "Warped Product Einstein Metrics Over Spaces with Constant Scalar Curvature" (2010). Mathematics - All Scholarship. 131.
https://surface.syr.edu/mat/131
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1012.3446