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arXiv · dg-ga/9712017

Jacobi vector fields of integrable geodesic flows

V. S. Matveev·P. J. Topalov
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Abstract

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental solution of the the Jacobi-Hill equation. This is done for quadratically integrable geodesic flows.

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BibTeXRIS

V. S. Matveev, P. J. Topalov. 1997-12-23. Jacobi vector fields of integrable geodesic flows. https://arxiv.org/abs/dg-ga/9712017

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