Definition:Isometry of Riemannian Manifold

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