Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 181, Pages 102–111
DOI: https://doi.org/10.36535/0233-6723-2020-181-102-111 (Mi into662) 		 
Locally Euclidean metrics and their isometric realizations

I. Kh. Sabitov

Lomonosov Moscow State University
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DOI: https://doi.org/10.36535/0233-6723-2020-181-102-111
Abstract: There are many works related to metrics and surfaces of positive and negative curvature. This paper is a survey of results related to locally Euclidean metrics and surfaces carrying such metrics. In this topic, there are many more problems included in the intersection of geometry, complex analysis, and differential equations that can become a source of new interesting research.
Keywords: locally Euclidean metric, natural representation, classification, isometric realization, developable surface, asymptotic coordinates, Monge—Ampère equation.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ 6222.2018.1
This work was supported by the Program of the President of the Russian Federation for Leading Scientific Schools of Russia (project NSh 6222.2018.1).
Bibliographic databases:
Document Type: Article
UDC: 53A05, 53C45
MSC: 53A05, 53C45
Language: Russian
Citation: I. Kh. Sabitov, “Locally Euclidean metrics and their isometric realizations”, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 181, VINITI, Moscow, 2020, 102–111
Citation in format AMSBIB
\Bibitem{Sab20}
\by I.~Kh.~Sabitov
\paper Locally Euclidean metrics and their isometric realizations
\inbook Proceedings of the International Conference "Classical and Modern Geometry"
Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev.
Moscow, April 22-25, 2019. Part 3
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 181
\pages 102--111
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into662}
\crossref{https://doi.org/10.36535/0233-6723-2020-181-102-111}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4208373}
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