Geodesic and metric completeness in infinite dimensions
type: Item
instance of: scholarly article
title: Geodesic and metric completeness in infinite dimensions
zbMATH Open document ID: 0871.58006
author: Christopher J. Atkin
published in: Hokkaido Mathematical Journal
publication date: 1997-10-06T00:00:00Z
review text: The main result of the paper is contained in the following Theorem A. There is a Riemannian manifold \(M\) such that: (i) \(M\) is modelled on a separable infinite-dimensional Hilbert space \(H\). (ii) \(M\) is of differentiability class \(C^\omega\). (iii) \(M\) is \(C^\omega\)-conformally equivalent to a Hilbert space \(H\). (iv) \(M\) is geodesically complete. (v) \(M\) is metrically incomplete. (vi) The metric completion of \(M\) has exactly one ideal point. (vii) \(M\) is geodesically convex (any two points of \(M\) may be joined by a minimizing geodesic). The proof, given in the last Section, is preceeded by many auxiliary propositions.
Mathematics Subject Classification ID: 58B20
zbMATH DE Number: 992413
zbMATH Keywords: infinite-dimensional manifold
zbMATH Keywords: geodesic completeness
zbMATH Keywords: metric completeness
zbMATH Keywords: Riemannian manifold
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351257804
OpenAlex ID: W2065368516
DOI: 10.14492/HOKMJ/1351257804
description: scientific article; zbMATH DE number 992413