Simple point

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Template:Point property in riemannian manifold

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.