Geodesic (mathematics)

thumb|Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns) In geometry, a geodesic () is a curve representing in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line".

generalization of straight line to a curved space time

mathematical measure in Riemannian geometry

Bending of trajectories in general relativity by a tidal force

shortest paths on a bounded deformed sphere-like quadric surface

theorem that every Riemannian manifold with the topology of a sphere has at least 3 closed geodesics

rigidity theorem in mathematics