Abstract
We introduce a notion of K-semistability for Sasakian manifolds. This extends to the irregular case of 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.
Citation
Tristan C. Collins. Gábor Székelyhidi. "K-semistability for irregular Sasakian manifolds." J. Differential Geom. 109 (1) 81 - 109, May 2018. https://doi.org/10.4310/jdg/1525399217