Email this article APPLICATION METHOD OF RIEMANN INVARIANTS TO SOLVE THE PROBLEM OF SURFACE RECONSTRUCTION ON THE SET OF NEGATIVE GAUSSIAN CURVATURE
- Authors: Fomicheva Y.G.1, Rudichenko A.A.1
-
Affiliations:
- Tambov State University named after G.R. Derzhavina
- Issue: Vol 21, No 6 (2016)
- Pages: 2068-2084
- Section: Articles
- URL: https://ogarev-online.ru/2686-9667/article/view/365984
- DOI: https://doi.org/10.20310/1810-0198-2016-21-6-2068-2084
- ID: 365984
Cite item
Full Text
Abstract
This paper addresses the question of recoverability in the three-dimensional Euclidean space with C 3 -regular surface explicitly specified by the equation z=z ( x, y ) on the entire plane of R 2 on its specified negative Gaussian curvature. The solution to this problem is reduced to the proof of existence and uniqueness of the R 2 of the classical solving differential equations of Monge-Ampere equations of hyperbolic type. Formulated the conditions for the existence of such a decision as a whole.
About the authors
Yuliya Gennadievna Fomicheva
Tambov State University named after G.R. Derzhavina
Email: fomichevajulia@mail.ru
Candidate of Physics and Mathematics, Associate Professor of the Functional Analysis Department Tambov, the Russian Federation
Anastasiya Andreevna Rudichenko
Tambov State University named after G.R. Derzhavina
Email: nastya2801@mail.ru
Master program student of the Functional Analysis Department Tambov, the Russian Federation
References
Бакельман И.Я., Вернер Л.А., Кантор Б.Е. Введение в дифференциальную геометрию «в целом». М.: Наука, 1973. Братков Ю.Н. О существовании классического решения гиперболического уравнения Монжа-Ампера в целом // Фундаментальная и прикладная математика. 2000. Т. 6. № 2. Туницкий Д.В. Системы в римановых инвариантах и уравнения Монжа-Ампера гиперболического типа // Деп.ВИНИТИ 16.07.87, № 5122-В87. Рождественский Б.Л., Яненко Н.Н. Системы квазилинейных уравнений и их приложений к газовой динамике. М.: Наука, 1978.
Supplementary files
