Definition:Isometric Immersion

Definition

Let $\struct {M, g}$, $\struct {\tilde M, \tilde g}$ be Riemannian manifolds.

Let $F : M \to \tilde M$ be an immersion such that $F^* \tilde g = g$.

Then $F$ is called an isometric immersion.

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Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Methods for Constructing Riemannian Metrics