4.5 Article

G-Sasaki Manifolds and K-Energy

期刊

JOURNAL OF GEOMETRIC ANALYSIS
卷 31, 期 2, 页码 1415-1470

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SPRINGER
DOI: 10.1007/s12220-019-00285-1

关键词

K-energy; Lie group; Sasaki– Einstein metrics

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This paper introduces a class of G-Sasaki manifolds with a reductive G-group action on their Kahler cones, proving the properness of K-energy on such manifolds and obtaining a sufficient and necessary condition for the existence of G-Sasaki-Einstein metrics. The results also apply to G-Sasaki-Ricci solitons, leading to the construction of many new examples through an established openness theorem.
In this paper, we introduce a class of Sasaki manifolds, called G-Sasaki manifolds with a reductive G-group action on their Kahler cones. By proving the properness of K-energy on such manifolds, we obtain a sufficient and necessary condition for the existence of G-Sasaki-Einstein metrics. A similar result is also obtained for G-Sasaki-Ricci solitons. As an application, we construct many new examples of G-Sasaki-Ricci solitons by an established openness theorem.

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