|
Matematicheskie Zametki, 2017, Volume 101, Issue 3, paper published in the English version journal
(Mi mzm11191)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
Papers published in the English version of the journal
Geodesics inMinimal Surfaces
Carlos M. C. Riveros, Armando M. V. Corro Universidade Federal de Goiás, Goiás, Brazil
Abstract:
In this paper, we consider connected minimal surfaces in
$\mathbb{R}^3$
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 $k_g^1$
and $k_g^2$
of the coordinates curves satisfy $\alpha k_g^1+\beta k_g^2=0$,
$\alpha$,
$\beta \in \mathbb{R}$.
Keywords:
minimal surfaces, geodesic curvature, lines of curvature.
Received: 16.02.2016
Citation:
Carlos M. C. Riveros, Armando M. V. Corro, “Geodesics inMinimal Surfaces”, Math. Notes, 101:3 (2017), 497–514
Linking options:
https://www.mathnet.ru/eng/mzm11191
|
Statistics & downloads: |
Abstract page: | 176 |
|