Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics

Details Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics

2011-04-21

arxiv.org/abs/1104.4314v1

Mathematics

Differential Geometry

28 pages

Scientific paper

We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L^2 metric. Among these we characterize a distinguished metric that can be regarded as a generalization of Calabi's metric on the space of K\"ahler metrics to the space of Riemannian metrics, and we study its geometry in detail. Unlike the Ebin metric, the geodesic equation involves non-local terms, and we solve it explicitly by using a constant of the motion. We then determine its completion, which gives the first example of a metric on the space of Riemannian metrics whose completion is strictly smaller than that of the Ebin metric.

Affiliated with

Also associated with

No associations

Rating

Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics 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 Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-178755