Definition:Isometry of Riemannian Manifold
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Definition
Let $\struct {M, g}$ be a Riemannian manifold.
Let $\phi : M \to M$ be an isometry such that:
- $\phi^* g = g$
Then $\phi$ is called the isometry of $\struct {M, g}$.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Definitions