Simple point

Definition

Symbol-free definition

A point on a Riemannian manifold is termed a simple point if it is not part of any geodesic loop.

Definition with symbols

A point $p$ in a Riemannian manifold $M$ is termed a simple point if there is no geodesic loop containing $p$.

Facts

Gromoll and Meyer proved that simple points exist provided the sectional curvature is positive everywhere.