Document Type
Article
Date
10-11-2011
Disciplines
Mathematics
Description/Abstract
In this paper we introduce a vector space of virtual warping functions that yield Einstein metrics over a fixed base. There is a natural quadratic form on this space and we study how this form interacts with the geometry. We use this structure along with the results in our earlier paper "Warped product rigidity" to show that essentially every warped product Einstein manifold admits a particularly nice warped product structure that we call basic. As applications we give a sharp characterization of when a homogeneous Einstein metric can be a warped product and also generalize a construction of Lauret showing that any algebraic soliton on a general Lie group can be extended to a left invariant Einstein metric.
Recommended Citation
He, Chenxu; Petersen, Peter; and Wylie, William, "The Space of Virtual Solutions to the Warped Product Einstein Equation" (2011). Mathematics - All Scholarship. 133.
https://surface.syr.edu/mat/133
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/1110.2456