On the transverse scalar curvature of a compact Sasaki manifold
arXiv:1105.4000
Abstract
We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in Kähler 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.
14 pages
References in corpus (4)
- Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
- Weighted projective embeddings, stability of orbifolds and constant scalar curvature Kähler metrics
- The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature
- Regularity of the geodesic equation in the space of Sasakian metrics