A CHARACTERIZATION OF THE CATENOID AND HELICOID

作者：Riveros Carlos M C^*; Corro Armando M V

来源：International Journal of Mathematics, 2013, 24(6): 1350045.

DOI：10.1142/S0129167X13500456

• Minimal surfaces
• Chebyshev net
• asymptotic lines
• lines of curvature

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.

• 出版日期2013-6