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December 2012 Surfaces with Constant Chebyshev Angle
Armando M. V. CORRO, Carlos M. C. RIVEROS
Tokyo J. Math. 35(2): 359-366 (December 2012). DOI: 10.3836/tjm/1358951324

Abstract

In this paper we consider surfaces with negative Gaussian curvature parametrized by a generalized Chebyshev net with constant Chebyshev angle in the Euclidean 3-space. We characterize these surfaces in terms of a meromorphic function which satisfies a certain differential equation. Moreover, we show that these surfaces have the geometric property that the asymptotic lines have the same sign of geodesic curvature. As an application we obtain for each constant Chebyshev angle a four-parameter family of complete surfaces.

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Armando M. V. CORRO. Carlos M. C. RIVEROS. "Surfaces with Constant Chebyshev Angle." Tokyo J. Math. 35 (2) 359 - 366, December 2012. https://doi.org/10.3836/tjm/1358951324

Information

Published: December 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1278.53013
MathSciNet: MR3058712
Digital Object Identifier: 10.3836/tjm/1358951324

Subjects:
Primary: 30D30
Secondary: 35C99, 53A10

Rights: Copyright © 2012 Publication Committee for the Tokyo Journal of Mathematics

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Vol.35 • No. 2 • December 2012
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