$G$-Sasaki manifolds and K-energy

Yan Li; Xiaohua Zhu

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arXiv · 1712.07934

$G$-Sasaki manifolds and K-energy

Yan Li·Xiaohua Zhu

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Abstract

In this paper, we introduce a class of Sasaki manifolds with a reductive $G$-group action, called $G$-Sasaki manifolds. By reducing K-energy to a functional defined on a class of convex functions on a moment polytope, we give a criterion for the properness of K-energy. In particular, we deduce a sufficient and necessary condition related to the polytope for the existence of transverse $G$-Sasaki Einstein metrics. A similar result is also obtained for transverse $G$-Sasaki Ricci solitons. As an application, we construct several examples of $G$-Sasaki Ricci solitons by an established openness theorem for transverse $G$-Sasaki Ricci solitons.

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Yan Li, Xiaohua Zhu. 2017-12-21. $G$-Sasaki manifolds and K-energy. https://arxiv.org/abs/1712.07934

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