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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Verpoort, S. Some modifications of the theorem of Beltrami. Annali di Matematica 190, 277–294 (2011). https://doi.org/10.1007/s10231-010-0150-5
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DOI: https://doi.org/10.1007/s10231-010-0150-5