Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds

Abstract

In this paper, we prove some rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals on closed manifolds, characterized by some point-wise inequalities. Moreover, we also provide a few rigidity results that involve the Weyl curvature, the trace-less Ricci curvature and the Yamabe invariant, accordingly.

arXiv commentAll comments are welcome

References in corpus (2)

• Rigidity theorems for compact Bach-flat manifolds with positive constant scalar curvature
• Rigidity of Riemannian manifolds with positive scalar curvature

Cited by in corpus (1)

• Rigidity of Einstein metrics as critical points of some quadratic curvature functionals on complete manifolds