conjugate points

Let M be a manifoldMathworldPlanetmath on which a notion of geodesicMathworldPlanetmath is defined. (For instance, M could be a Riemannian manifoldMathworldPlanetmath, M could be a manifold with affine connectionMathworldPlanetmath, or M could be a Finsler space.)

Two distinct points, P and Q of M are said to be conjugate points if there exist two or more distinct geodesic segments having P and Q as endpointsMathworldPlanetmath.

A simple example of conjugate points are the north and south polesMathworldPlanetmath of a sphere (endowed with the usual metric of constant curvature) — every meridianMathworldPlanetmath is a geodesic segment having the poles as endpoints.

Title conjugate points
Canonical name ConjugatePoints
Date of creation 2013-03-22 14:35:40
Last modified on 2013-03-22 14:35:40
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 5
Author rspuzio (6075)
Entry type Definition
Classification msc 53B05