Some Modifications of the Theorem of Beltrami

• Autoři: VERPOORT Steven J.
• Rok publikování: 2011
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Annali di Matematica Pura ed Applicata
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Doi: https://doi.org/10.1007/s10231-010-0150-5
• Obor: Obecná matematika
• Klíčová slova: Theorem of Beltrami
• Popis: 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.

Související projekty

• Centrum Eduarda Čecha pro algebru a geometrii