
Review of Short Phrases and Links 
This Review contains major "Jacobi Field" related terms, short phrases and links grouped together in the form of Encyclopedia article.
 A field J is a Jacobi field if and only if it satisfies the Jacobi equation: where D denotes the LeviCivita connection, R the curvature tensor and.
 For Riemannian manifolds of constant negative curvature  k 2, any Jacobi field is a linear combination of, and, where i 1.
 Conjugate points two points p and q on a geodesic γ are called conjugate if there is a Jacobi field on γ which has a zero at p and q.
 The restriction of a Killing field to a geodesic is a Jacobi field in any Riemannian manifold.
 In Riemannian geometry, a Jacobi field is a certain type of vector field along a geodesic γ in a Riemannian manifold.
 The restriction of a Killing vector field to a geodesic is a Jacobi field in any Riemannian manifold.
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Jacobi Field
 Further, the sum of Jacobi fields on a given geodesic is again a Jacobi field.
 On a complete Riemannian manifold, for any Jacobi field there is a family of geodesics γ τ describing the field (as in the preceding paragraph).
 Conjugate point two points p and q on a geodesic γ are called conjugate if there is a Jacobi field on γ which has a zero at p and q.
Categories
 Complete Riemannian Manifold
 Geodesic
 Jacobi Fields
 Conjugate Points
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