Difference between revisions of "Jacobi field"
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Latest revision as of 19:47, 18 May 2008
Definition
Let be a Riemannian manifold.
A vector field along a curve is termed a Jacobi field if it satisfies the following equation:
where is the tangent vector field along the curve.
The above is a secondorder differential equations called the Jacobi equation.
Facts
Jacobi fields are precisely the null space of the positive semidefinite quadratic form which is defined as:
where are variations with variation vector field .