# conjugate points

Let $M$ be a manifold^{} on which a notion of geodesic^{} is defined. (For instance, $M$ could be a Riemannian manifold^{}, $M$ could be a manifold with affine connection^{}, 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 endpoints^{}.

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

Title | conjugate points |
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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 |