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ON THE LOCAL RIGIDITY OF EINSTEIN MANIFOLDS WITH CONVEX BOUNDARY

By Michael T. Anderson

Abstract

Abstract. Let (M, g) be a compact Einstein manifold with non-empty boundary ∂M. We prove that Killing fields at ∂M extend to Killings fields of (any) (M, g) provided ∂M is (weakly) convex and π1(M, ∂M) = {e}. This gives a new proof of the classical infinitesimal rigidity of convex surfaces in Euclidean space and generalizes the result to Einstein metrics of any dimension. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.8898
Provided by: CiteSeerX
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