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- Title
Pseudocomplete Riemannian Analytic Manifolds.
- Authors
Popov, V. A.
- Abstract
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 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.
- Subjects
RIEMANNIAN metric; LIE groups; RIEMANNIAN manifolds; VECTOR fields; LIE algebras
- Publication
Mathematical Notes, 2023, Vol 114, Issue 5/6, p895
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S000143462311024X