The space of virtual solutions to the warped product Einstein equation

Details The space of virtual solutions to the warped product Einstein equation The space of virtual solutions to the warped product Einstein equation

2011-10-11

arxiv.org/abs/1110.2456v1

Mathematics

Differential Geometry

39 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The space of virtual solutions to the warped product Einstein equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The space of virtual solutions to the warped product Einstein equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The space of virtual solutions to the warped product Einstein equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-472482