Journal of Differential Geometry

K-semistability for irregular Sasakian manifolds

Tristan C. Collins and Gábor Székelyhidi

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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.

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

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

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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.

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