Relative K-stability and extremal Sasaki metrics
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Publication:722885
DOI10.4310/MRL.2018.V25.N1.A1zbMATH Open1400.53034arXiv1608.06184MaRDI QIDQ722885
Author name not available (Why is that?)
Publication date: 30 July 2018
Published in: (Search for Journal in Brave)
Abstract: We define K-stability of a polarized Sasakian manifold relative to a maximal torus of automorphisms. The existence of a Sasaki-extremal metric in the polarization is shown to imply that the polarization is K-semistable. Computing this invariant for the deformation to the normal cone gives an extention of the Lichnerowicz obstruction, due to Gauntlett, Martelli, Sparks, and Yau, to an obstruction of Sasaki-extremal metrics. We use this to give a list of examples of Sasakian manifolds whose Sasaki cone contains no extremal representatives. These give the first examples of Sasaki cones of dimension greater than one that contain no extremal Sasaki metrics whatsoever. In the process we compute the unreduced Sasaki cone for an arbitrary smooth link of a weighted homogeneous polynomial.
Full work available at URL: https://arxiv.org/abs/1608.06184
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