Definition:Pseudo-Riemannian Manifold

Definition

A pseudo-Riemannian manifold is a smooth manifold on the real space $\R^{r+s}$ upon which a pseudo-Riemannian metric has been imposed.

Dimension

The dimension of the pseudo-Riemannian manifold on $\R^{r + s}$ is $r + s$.

Also see

• Results about pseudo-Riemannian manifolds can be found here.

• Definition:Riemannian Manifold

Source of Name

This entry was named for Bernhard Riemann.

Sources

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