Isotropic at Point and Homogeneous Riemannian Manifold is Isotropic

Theorem

Let $\struct {M, g}$ be a Riemannian manifold.

Let $M$ be isotropic at any $p \in M$.

Let $M$ be homogeneous.

Then $M$ is isotropic.

Proof

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Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 3$: Model Riemannian Manifolds. Symmetries of Riemannian Manifolds