Jacobi vector fields of integrable geodesic flows

Details Jacobi vector fields of integrable geodesic flows Jacobi vector fields of integrable geodesic flows

1997-12-23

arxiv.org/abs/dg-ga/9712017v1

Regular and Chaotic Dynamics vol 2 no 1 (1997) 103-116

Mathematics

Differential Geometry

15 pages, latex2e, 2 Postscript figures included

Scientific paper

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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