Frame-Homogeneous Riemannian Manifold is Homogeneous and Isotropic
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Theorem
Let $\struct {M, g}$ be a Riemannian manifold.
Suppose $M$ is frame-homogeneous.
Then $M$ is homogeneous and 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