Conjugate points: Difference between revisions

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Revision as of 13:35, 1 March 2019

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In [[differential geometry]], '''conjugate points''' are, roughly, points that can almost be joined by a 1-parameter family of [[geodesic]]s. For example, on a [[Spherical geometry|sphere]], the north-pole and south-pole are connected by any [[Meridian (geography)|meridian]]. Another viewpoint is that conjugate points tell when the geodesics fail to be length-minimizing. Geodesics are locally length-minimizing, but, for example, on a sphere, any geodesic from the north-pole fail to be length-minimizing if it passes through the south-pole.<ref>Cheeger, Ebin. ''Comparison Theorems in Riemannian Geometry''. North-Holland Publishing Company, 1975, pp. 17-18.</ref>

==Definition==

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* [[Cut locus (Riemannian manifold)|Cut locus]]

* [[Jacobi field]]

==References==

{{Reflist}}

{{DEFAULTSORT:Conjugate Points}}