= Cartan-Ambrose-Hicks theorem
{c}
{wiki=Cartan–Ambrose–Hicks_theorem}
A linear <isometry> between tangent spaces of complete simply connected <Riemannian manifolds> extends to a global <isometry> when parallel transport along corresponding broken <geodesics> identifies their <Riemann curvature tensors>. In particular, complete simply connected manifolds of the same dimension and constant <sectional curvature> are isometric: their curvature tensors are determined by that common constant and their <Riemannian metrics>. This is the constant-curvature form often called Cartan's theorem.
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