Some Modifications of the Theorem of Beltrami

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Authors

VERPOORT Steven J.

Year of publication 2011
Type Article in Periodical
Magazine / Source Annali di Matematica Pura ed Applicata
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1007/s10231-010-0150-5
Field General mathematics
Keywords Theorem of Beltrami
Description 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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