A CHARACTERIZATION OF THE CATENOID AND HELICOID-Reference-Cited by-同舟云学术

A CHARACTERIZATION OF THE CATENOID AND HELICOID

Published:2013-06 Issue:06 Volume:24 Page:1350045
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

RIVEROS CARLOS M. C.¹,CORRO ARMANDO M. V.²

Affiliation:

1. Departamento de Matemática, Universidade de Brasília, 70910-900, Brasília-DF, Brazil

2. Instituto de Matemática e Estatística, Universidade Federal de Goiâs, 74001-970, Goiânia-GO, Brazil

Abstract

In this paper we show that a connected non-planar minimal surface whose asymptotic lines have the same geodesic curvature up to sign is a catenoid. As an application of this result we show that a connected non-planar minimal surface whose lines of curvature have the same geodesic curvature up to sign is a helicoid. Moreover, we show that the coordinates curves of the associate minimal surfaces to catenoid have the same geodesic curvature up to sign.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X13500456

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