On the Local Rigidity of Einstein Manifolds with Convex Boundary
نویسنده
چکیده
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.
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تاریخ انتشار 2013