On the geometry of Riemannian cubic polynomials. (Q1397822)
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scientific article; zbMATH DE number 1959882
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the geometry of Riemannian cubic polynomials. |
scientific article; zbMATH DE number 1959882 |
Statements
On the geometry of Riemannian cubic polynomials. (English)
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6 August 2003
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The aim of this paper is to characterize the local minimizers among the generalized cubic polynomials for a functional expressed by the covariant acceleration on a finite-dimensional Riemannian manifold. Inspired by the theory of geodesics, necessary and sufficient optimality conditions are obtained in terms of generalized notions of Jacobi fields and conjugate points.
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Riemannian manifolds
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cubic polynomials
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second variation
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Jacobi fields
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conjugate points
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