Some modifications of the theorem of Beltrami |
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Authors: | Steven Verpoort |
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Affiliation: | 1.Departement Wiskunde,Katholieke Universiteit Leuven,Heverlee,Belgium;2.ústav Matematiky a Statistiky,Masarykova Univerzita,Brno,Czech Republic |
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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. |
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