K-Semistability for irregular Sasakian manifolds

Details K-Semistability for irregular Sasakian manifolds K-Semistability for irregular Sasakian manifolds

2012-04-10

arxiv.org/abs/1204.2230v1

Mathematics

Differential Geometry

25 pages

Scientific paper

We introduce a notion of K-semistability for Sasakian manifolds. This extends to the irregular case the orbifold K-semistability of Ross-Thomas. Our main result is that a Sasakian manifold with constant scalar curvature is necessarily K-semistable. As an application, we show how one can recover the volume minimization results of Martelli-Sparks-Yau, and the Lichnerowicz obstruction of Gauntlett-Martelli-Sparks-Yau from this point of view.

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