Energy properness and Sasakian-Einstein metrics

Details Energy properness and Sasakian-Einstein metrics Energy properness and Sasakian-Einstein metrics

2010-07-15

arxiv.org/abs/1007.2626v1

Commun.Math.Phys.306:229-260,2011

Mathematics

Differential Geometry

27 pages

Scientific paper

10.1007/s00220-011-1292-z

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.

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