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Title: Two-dimensional manifolds with metrics of revolution

Abstract

This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R{sup 3} other than a sphere and a torus (moreover, in the smoothness class C{sup {infinity}} such surfaces, understood in a certain generalized sense, exist in any topological class)

Authors:
 [1]
  1. M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
21202960
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 191; Journal Issue: 10; Other Information: DOI: 10.1070/SM2000v191n10ABEH000517; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; METRICS; SMOOTH MANIFOLDS; SPHERES; SURFACES; TOPOLOGY; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Sabitov, I Kh. Two-dimensional manifolds with metrics of revolution. United States: N. p., 2000. Web. doi:10.1070/SM2000V191N10ABEH000517; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Sabitov, I Kh. Two-dimensional manifolds with metrics of revolution. United States. https://doi.org/10.1070/SM2000V191N10ABEH000517; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Sabitov, I Kh. 2000. "Two-dimensional manifolds with metrics of revolution". United States. https://doi.org/10.1070/SM2000V191N10ABEH000517; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21202960,
title = {Two-dimensional manifolds with metrics of revolution},
author = {Sabitov, I Kh},
abstractNote = {This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R{sup 3} other than a sphere and a torus (moreover, in the smoothness class C{sup {infinity}} such surfaces, understood in a certain generalized sense, exist in any topological class)},
doi = {10.1070/SM2000V191N10ABEH000517; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
url = {https://www.osti.gov/biblio/21202960}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 10,
volume = 191,
place = {United States},
year = {Tue Oct 31 00:00:00 EST 2000},
month = {Tue Oct 31 00:00:00 EST 2000}
}