Definition:Pseudo-Riemannian Submanifold

Definition

Let $\struct {\tilde M, \tilde g}$ be a pseudo-Riemannian manifold.

Let $i : \tilde M \to M$ be a smooth submanifold, where $i$ is the inclusion mapping.

Suppose $i^* \tilde g$ is nondegenerate with constant signature.

Then $\struct {M, i^* \tilde g}$ is called the pseudo-Riemannian submanifold (of $\struct {\tilde M, \tilde g}$).

Sources

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