Riemannian Rigidity of the Parallel Postulate in Total Curvature
Differential Geometry
2016-11-24 v1
Abstract
We prove that the Euclidean plane is the only Riemannian plane with total curvature and free of conjugate points that satisfies Playfair's version of the parallel postulate.
Keywords
Cite
@article{arxiv.1611.07761,
title = {Riemannian Rigidity of the Parallel Postulate in Total Curvature},
author = {Jian Ge and Luis Guijarro and Pedro Solórzano},
journal= {arXiv preprint arXiv:1611.07761},
year = {2016}
}