Geodesics in minimal surfaces
- Авторлар: Riveros C.M.1, Corro A.M.2
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Мекемелер:
- Universidade de Brasília
- Universidade Federal de Goiâs
- Шығарылым: Том 101, № 3-4 (2017)
- Беттер: 497-514
- Бөлім: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/150012
- DOI: https://doi.org/10.1134/S0001434617030129
- ID: 150012
Дәйексөз келтіру
Аннотация
Abstract—In this paper, we consider connected minimal surfaces in R3 with isothermal coordinates and with a family of geodesic coordinates curves, these surfaces will be called GICM-surfaces. We give a classification of the GICM-surfaces. This class of minimal surfaces includes the catenoid, the helicoid and Enneper’s surface. Also, we show that one family of this class of minimal surfaces has at least one closed geodesic and one 1-periodic family of this class has finite total curvature. As application we show other characterization of catenoid and helicoid. Finally, we show that the class of GICM-surfaces coincides with the class of minimal surfaces whose the geodesic curvature kg1 and kg2 of the coordinates curves satisfy αkg1 + βkg2 = 0, α, β ∈ R.
Негізгі сөздер
Авторлар туралы
Carlos Riveros
Universidade de Brasília
Хат алмасуға жауапты Автор.
Email: carlos@mat.unb.br
Бразилия, Brasília
Armando Corro
Universidade Federal de Goiâs
Email: carlos@mat.unb.br
Бразилия, Goiânia
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