Jacobi vector fields of integrable geodesic flows
dg-ga
2011-08-22 v1 微分几何
摘要
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.
引用
@article{arxiv.dg-ga/9712017,
title = {Jacobi vector fields of integrable geodesic flows},
author = {V. S. Matveev and P. J. Topalov},
journal= {arXiv preprint arXiv:dg-ga/9712017},
year = {2011}
}
备注
15 pages, latex2e, 2 Postscript figures included