Some Modifications of the Theorem of Beltrami

Details Some Modifications of the Theorem of Beltrami Some Modifications of the Theorem of Beltrami

2009-12-21

arxiv.org/abs/0912.4064v1

Mathematics

Differential Geometry

19 pages, 3 figures

Scientific paper

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.

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