arXiv 0912.40642009-12-21math.DG

Some Modifications of the Theorem of Beltrami

Steven Verpoort

备注：: 19 pages, 3 figures

英文摘要：

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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