Rigidity and the distance between boundary points
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.
complete Riemannian metric without conjugate points
scientific article; zbMATH DE number 4205315