On the transverse scalar curvature of a compact Sasaki manifold

Details On the transverse scalar curvature of a compact Sasaki manifold On the transverse scalar curvature of a compact Sasaki manifold

2011-05-20

arxiv.org/abs/1105.4000v1

ARXIV:1105.4000

Mathematics

Differential Geometry

14 pages

Scientific paper

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.

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