On the transverse Scalar Curvature of a Compact Sasaki Manifold

Complex Manifolds

He Weiyong¹ 

[1] Department of Mathematics, University of Oregon, Eugene, OR, 97403;

关键词: transverse scalar curvature;    symmetric space;    moment map;   

DOI  :  10.2478/coma-2014-0004

来源: DOAJ

【 摘 要 】

We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in Kähler geometry described by S.K. Donaldson [10, 11], which involves the geometry of infinitedimensional 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

【 授权许可】

Unknown