Definition:Riemannian Submanifold

Definition

Let $M$ be an immersed submanifold with or without a boundary.

Let $g$ be a metric induced on $M$.

Then $\struct {M, g}$ is called the Riemannian submanifold.

Sources

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