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 with such metrics. There are many problems included in the intersection of geometry, complex analysis, and differential equations that can become a source of new interesting research.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 181, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor V. T. Bazylev. Moscow, April 22-25, 2019. Part 3, 2020.
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Sabitov, I.K. Locally Euclidean Metrics and their Isometric Realizations. J Math Sci 276, 793–801 (2023). https://doi.org/10.1007/s10958-023-06802-6
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DOI: https://doi.org/10.1007/s10958-023-06802-6
Keywords and phrases
- locally Euclidean metric
- natural representation
- classification
- isometric realization
- developable surface
- asymptotic coordinates
- Monge—Ampère equation
- 53A05
- 53C45