A dual rigidity of the sphere and the hyperbolic plane

2015/05/20 by Magdalena Caballero, Caballero, Magdalena, Rafael M. Rubio +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1505.05446

arxiv created 2015/05/20 · arxiv updated 2015/05/21

Abstract

There are several well-known characterizations of the sphere as a regular surface in the Euclidean space. By means of a purely synthetic technique, we get a rigidity result for the sphere without any curvature conditions, nor completeness or compactness. As well as a dual result for the hyperbolic plane, the spacelike sphere in the Minkowski space.

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