Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds
Differential Geometry
2018-05-01 v1
Abstract
In this paper, we consider some rigidity results for the Einstein metrics as the critical points of some known quadratic curvature functionals on complete manifolds, characterized by some point-wise inequalities. Moreover, we also provide rigidity results by the integral inequalities involving the Weyl curvature, the trace-less Ricci curvature and the Sobolev constant, accordingly.
Keywords
Cite
@article{arxiv.1804.10748,
title = {Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds},
author = {Guangyue Huang and Yu Chen and Xingxiao Li},
journal= {arXiv preprint arXiv:1804.10748},
year = {2018}
}
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