The Jacobi map (Q1924397)
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scientific article; zbMATH DE number 936182
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Jacobi map |
scientific article; zbMATH DE number 936182 |
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The Jacobi map (English)
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16 December 1996
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Using two-parameter variations of a geodesic in a semi-Riemannian manifold, the author introduces \(n\)-th order Jacobi vector fields. He obtains necessary and sufficient conditions for an \(n\)-th order Jacobi field to be the variation vector field as well as the index theorem, giving upper and lower bounds for the focal multiplicity.
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geodesic variation
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Jacobi field
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semi-Riemannian manifold
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index theorem
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