2009/12/21 by Steven Verpoort, Verpoort, Steven
Mathematics · #53B20 #53B25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B20 #msc:53B25
paper · pdf · doi:10.48550/arxiv.0912.4064
19 pages, 3 figures
arxiv created 2009/12/21 · arxiv updated 2010/01/14
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.