Approximating Riemannian manifolds by polyhedra
Differential Geometry
2023-08-11 v2
Abstract
This is a study on approximating a Riemannian manifold by polyhedra. Our scope is understanding Tullio Regge's [52] article in the restricted Riemannian frame. We give a proof of the Regge theorem along lines close to its original intuition: one can approximate a compact domain of a Riemannian manifold by polyhedra in such a way that the integral of the scalar curvature is approximated by a corresponding polyhedral curvature.
Cite
@article{arxiv.2204.09536,
title = {Approximating Riemannian manifolds by polyhedra},
author = {Daniel Meyer and Eric Toubiana},
journal= {arXiv preprint arXiv:2204.09536},
year = {2023}
}