Document Type

Article

Date

10-11-2011

Embargo Period

11-18-2011

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.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1110.2456

Source

Harvested from arXiv.org

Creative Commons License


This work is licensed under a Creative Commons Attribution 3.0 License.

Included in

Mathematics Commons

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