On the transverse scalar curvature of a compact Sasaki manifold

ARXIV:1105.4000 We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in K\"ahler geometry described by S.K. Donaldson, which involves the geometry of infinite-dimensional groups and spaces, can be applied to the constant scalar curvature metri...

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Bibliographic Details
Main Author He, Weiyong
Format Journal Article
LanguageEnglish
Published 19.05.2011
Subjects
Mathematics - Differential Geometry
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Summary:ARXIV:1105.4000 We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in K\"ahler geometry described by S.K. Donaldson, which involves the geometry of infinite-dimensional groups and spaces, can be applied to the constant scalar curvature metrics in Sasaki geometry with only few modification. We prove that the space of Sasaki metrics is an infinite dimensional symmetric space and that the transverse scalar curvature of a Sasaki metric is a moment map of the strict contactomophism group.
DOI:10.48550/arxiv.1105.4000