Definition:Geodesically Complete Semi-Riemannian Manifold

Definition
Let $\struct {M, g}$ be a semi-Riemannian manifold.

Let $I$ be an real interval.

Suppose every maximal geodesic $\gamma : I \ni t \to M$ is defined for all $t \in \R$.

That is, suppose that every maximal geodesic in $M$ is a geodesic $\gamma : \R \to M$.

Then $M$ is geodesically complete.