= Homogeneous Riemannian manifold
= Riemannian homogeneous space
{c}
{synonym}
A <Riemannian manifold> is homogeneous when its <isometry> group acts transitively on points. For example, a <Lie group> with a <left-invariant metric> is homogeneous under left translations. Homogeneity gives the same local metric-ball geometry at every point, which yields the <completeness of homogeneous Riemannian manifolds>. It does not imply two-point homogeneity: that stronger property also controls directions and pairs at equal distance.
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