Canonical Sasakian Metrics

Details Canonical Sasakian Metrics Canonical Sasakian Metrics

2006-04-13

arxiv.org/abs/math/0604325v2

Commun.Math.Phys.279:705-733,2008

Mathematics

Differential Geometry

36 pages, minor corrections made, example added

Scientific paper

10.1007/s00220-008-0429-1

Let $M$ be a closed manifold of Sasaki type. A polarization of $M$ is defined by a Reeb vector field, and for one such, we consider the set of all Sasakian metrics compatible with it. On this space, we study the functional given by the squared $L^2$-norm of the scalar curvature. We prove that its critical points, or canonical representatives of the polarization, are Sasakian metrics that are transversally extremal. We define a Sasaki-Futaki invariant of the polarization, and show that it obstructs the existence of constant scalar curvature representatives. For a fixed CR structure of Sasaki type, we define the Sasaki cone of structures compatible with this underlying CR structure, and prove that the set of polarizations in it that admit a canonical representative is open.

Affiliated with

Also associated with

No associations

Rating

Canonical Sasakian 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 Canonical Sasakian Metrics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Canonical Sasakian Metrics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-623831