Energy properness and Sasakian-Einstein metrics
Differential Geometry
2011-07-21 v1
Abstract
In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.
Keywords
Cite
@article{arxiv.1007.2626,
title = {Energy properness and Sasakian-Einstein metrics},
author = {Xi Zhang},
journal= {arXiv preprint arXiv:1007.2626},
year = {2011}
}
Comments
27 pages