= Two-point homogeneous Riemannian manifold
= Two-point homogeneity
{synonym}
A connected <Riemannian manifold> is two-point homogeneous if its <isometry> group is transitive on ordered pairs at each fixed <Riemannian distance>. The equal-distance condition is necessary because <isometries> preserve distance. Round spheres and Euclidean spaces are examples. The <unit tangent transitivity characterizes two-point homogeneity> lemma shows that this pair condition is equivalent to transitivity on the <unit tangent bundle>.
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