Geodesic and metric completeness in infinite dimensions
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.
scientific article; zbMATH DE number 992413