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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 19, 2014

On the transverse Scalar Curvature of a Compact Sasaki Manifold

Weiyong He
From the journal Complex Manifolds

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 [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

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Received: 2013-10-14
Accepted: 2014-04-18
Published Online: 2014-09-19

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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