Calculus of Variations and Geometric Measure Theory
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G. Catino

Some rigidity results on critical metrics for quadratic functionals

created by catino on 02 Apr 2014
modified on 10 Apr 2016


Published Paper

Inserted: 2 apr 2014
Last Updated: 10 apr 2016

Journal: Calc. Var. Partial Differential Equations
Volume: 54
Number: 3
Pages: 2921-2937
Year: 2015


In this paper we prove rigidity results on critical metrics for quadratic curvature functionals, involving the Ricci and the scalar curvature, on the space of Riemannian metrics with unit volume. It is well-known that Einstein metrics are always critical points. The purpose of this article is to show that, under some curvature conditions, a partial converse is true. In particular, for a class of quadratic curvature functionals, we prove that every critical metric with non-negative sectional curvature must be Einstein.


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