In mathematics, the Cartan–Ambrose–Hicks theorem is a theorem of Riemannian geometry, according to which the Riemannian metric is locally determined by...

spaces, and so these are locally parallelizable; this is the Cartan–Ambrose–Hicks theorem. Killing vector fields can be generalized to conformal Killing...

theory Cartan–Ambrose–Hicks theorem Cartan–Brauer–Hua theorem Cartan–Dieudonné theorem Cartan–Hadamard manifold Cartan–Hadamard theorem Cartan–Iwahori...

affine transformations. This equivalence is an easy corollary of Cartan–Ambrose–Hicks theorem. Equivalently, it is a manifold equipped with an atlas—called...

geodesic symmetries can be extended to isometries on all of M. The Cartan–Ambrose–Hicks theorem implies that M is locally Riemannian symmetric if and only if...