an:06476701
Zbl 1323.53047
He, Weiyong
On the transverse scalar curvature of a compact Sasaki manifold
EN
Complex Manifolds 1, 52-63 (2014).
00347707
2014
j
53C25 53C35 58B25
transverse scalar curvature; symmetric space; moment map
Summary: We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in K??hler 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.