Extension of symmetries on Einstein manifolds with boundary |
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Authors: | Michael T Anderson |
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Institution: | 1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, USA
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Abstract: | We investigate the validity of the isometry extension property for (Riemannian) Einstein metrics on compact manifolds M with boundary ∂M. Given a metric γ on ∂M, this is the issue of whether any Killing field X of (∂M, γ) extends to a Killing field of any Einstein metric (M, g) bounding (∂M, γ). Under a mild condition on the fundamental group, this is proved to be the case at least when X preserves the mean curvature of ∂M in (M, g). |
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