Pseudocomplete Riemannian Analytic Manifolds

We study the analytic extension of a locally given Riemannian analytic metric to a metric of a nonextendable manifold. Various classes of locally isometric Riemannian analytic manifolds are studied. In each of these classes, the notion of the so-called pseudocomplete manifold is defined, which generalizes the notion of completeness of a manifold. A Riemannian analytic simply connected oriented manifold $M$ is said to be pseudocomplete if it is nonextendable and there exists no locally isometric orientation-preserving covering mapping with a simply connected Riemannian manifold. Among the pseudocomplete manifolds, we single out the “most symmetric” regular pseudocomplete manifolds.