﻿ "Jacobi Field" related terms, short phrases and links

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### FieldUpDw('FIELD','-Abz-');

1. A field J is a Jacobi field if and only if it satisfies the Jacobi equation: where D denotes the Levi-Civita connection, R the curvature tensor and.

### Riemannian ManifoldsUpDw('RIEMANNIAN_MANIFOLDS','-Abz-');

1. For Riemannian manifolds of constant negative curvature - k 2, any Jacobi field is a linear combination of, and, where i 1.

### Conjugate PointsUpDw('CONJUGATE_POINTS','-Abz-');

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.

### GeodesicUpDw('GEODESIC','-Abz-');

1. The restriction of a Killing field to a geodesic is a Jacobi field in any Riemannian manifold.
2. In Riemannian geometry, a Jacobi field is a certain type of vector field along a geodesic γ in a Riemannian manifold.
3. The restriction of a Killing vector field to a geodesic is a Jacobi field in any Riemannian manifold. (Web site)

### Jacobi FieldUpDw('JACOBI_FIELD','-Abz-');

1. Further, the sum of Jacobi fields on a given geodesic is again a Jacobi field.
2. 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).
3. 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.

### CategoriesUpDw('Categories','-Abz-');

1. Complete Riemannian Manifold
2. Geodesic
3. Jacobi Fields
4. Conjugate Points
5. Preceding Paragraph
6. Books about "Jacobi Field" in Amazon.com
 Short phrases about "Jacobi Field"   Originally created: May 21, 2008.   Links checked: June 26, 2013.   Please send us comments and questions by this Online Form   Please click on to move good phrases up.
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