Rigidity and the distance between boundary points
type: Item
instance of: scholarly article
title: Rigidity and the distance between boundary points
zbMATH Open document ID: 0729.53043
author: Christopher B. Croke
published in: Journal of Differential Geometry
publication date: 1991-01-01T00:00:00Z
review text: Several rigidity results for Riemannian manifolds are proved. For example it is shown that any complete Riemannian metric without conjugate points on \({\mathbb{R}}^ n\) which is isometric to the Euclidean metric outside a compact set is isometric to the Euclidean metric. The results of the paper are related to the following ``boundary rigidity problem'' for a compact Riemannian manifold M with boundary H: Under which assumptions does the induced distance function d: \(H\times H\to {\mathbb{R}}\) determine the metric on M uniquely? This problem was studied earlier by R. Michel and M. Gromov.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 4205315
zbMATH Keywords: minimizing geodesics
zbMATH Keywords: rigidity results
zbMATH Keywords: complete Riemannian metric without conjugate points
zbMATH Keywords: boundary rigidity problem
zbMATH Keywords: distance function
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214446326
OpenAlex ID: W1549087646
Wikidata QID: Q115181659
DOI: 10.4310/JDG/1214446326
description: scientific article; zbMATH DE number 4205315