Journal of Differential Geometry

K-semistability for irregular Sasakian manifolds

Tristan C. Collins and Gábor Székelyhidi

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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.

Article information

Source
J. Differential Geom., Volume 109, Number 1 (2018), 81-109.

Dates
Received: 16 July 2012
First available in Project Euclid: 4 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1525399217

Digital Object Identifier
doi:10.4310/jdg/1525399217

Mathematical Reviews number (MathSciNet)
MR3798716

Zentralblatt MATH identifier
06868031

Citation

Collins, Tristan C.; Székelyhidi, Gábor. K-semistability for irregular Sasakian manifolds. J. Differential Geom. 109 (2018), no. 1, 81--109. doi:10.4310/jdg/1525399217. https://projecteuclid.org/euclid.jdg/1525399217


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