Some Modifications of the Theorem of Beltrami
Differential Geometry
2009-12-22 v1
Abstract
The two main topics of this text are as follows: Firstly, three modifications of the theorem of Beltrami will be presented for diffeomorphisms between Riemannian manifolds and a space form which preserve the geodesic circles, the geodesic hyperspheres, or the minimal surfaces, respectively. Secondly, it is defined what it means for an infinitesimal deformation of a metric to preserve the geodesics up to first order, and a corresponding infinitesimal version of Beltrami's theorem is given.
Keywords
Cite
@article{arxiv.0912.4064,
title = {Some Modifications of the Theorem of Beltrami},
author = {Steven Verpoort},
journal= {arXiv preprint arXiv:0912.4064},
year = {2009}
}
Comments
19 pages, 3 figures