Definition:Closed Geodesic

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

Let $I = \closedint a b$ be a close real interval.

Let $\gamma : I \to M$ be a nonconstant geodesic segment.

Suppose:


 * $\map \gamma a = \map \gamma b$


 * $\map {\gamma'} a = \map {\gamma'} b$

where $\gamma'$ is the velocity of $\gamma$.

Then $\gamma$ is said to be a closed geodesic.