Pseudocompleet rumanian analytic manifold

Abstract

We study the analytic extension of a locally given Riemannian analytic metric to the metric of non-extendable manifolds. Various classes of locally isometric Riemannian analytic manifolds are studied. In each such class, the notion of the so-called pseudocomplete manifold is defined, which generalizes the notion of the completeness of a manifold. Riemannian analytic simply connected oriented manifold M is called pseudocomplete if it has the following properties. M is unextendable. There is no locally isometric orientation-preserving covering map f : M → N, where N is a simply connected oriented Riemannian analytic manifold and f (M) is an open subset of N not equal to N. Among the pseudocomplete manifolds, we single out the “most symmetric” regular pseudocomplete manifolds.