46. Isometric maps and natural Riemannian connections
We define the notion of an isometric map between Riemannian manifolds, and investigate how the Levi-Civita connection behaves with respect to isometric maps.
We conclude by stating a theorem of Epstein from 1978 which shows that, under two additional “reasonable” conditions, the Levi-Civita connection is the unique connection that behaves nicely with respect to isometries.
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