Geodesic
Locally Euclidean metrics and their isometric realizations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 181 (2020), pp. 102-111.

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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, isometric realization, developable surface, asymptotic coordinates, Monge—Ampère equation.
Mots-clés : classification 
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I. Kh. Sabitov. Locally Euclidean metrics and their isometric realizations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 181 (2020), pp. 102-111. http://geodesic.mathdoc.fr/item/INTO_2020_181_a11/

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