1. A CHARACTERIZATION OF THE CATENOID AND HELICOID.
- Author
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HIVEROS, CARLOS M. C. and CORRO, ARMANDO M. V.
- Subjects
- *
MINIMAL surfaces , *ASYMPTOTES , *GEODESICS , *CURVATURE , *GEOMETRIC surfaces , *MATHEMATICAL analysis - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2013
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