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October, 2000 Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space
Reiko AIYAMA, Kazuo AKUTAGAWA
J. Math. Soc. Japan 52(4): 877-898 (October, 2000). DOI: 10.2969/jmsj/05240877

Abstract

Our primary object of this paper is to give a representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space of curvature -1 in terms of their normal Gauss maps. For CMC (constant mean curvature) surfaces, we derive another representation formula in terms of their adjusted Gauss maps. These formulas are hyperbolic versions of the Kenmotsu representation formula for surfaces in the Euclidean 3-space. As an application, we give a construction of complete simply connected CMC H(|H|<1) surfaces embedded in the hyperbolic 3-space.

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Reiko AIYAMA. Kazuo AKUTAGAWA. "Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space." J. Math. Soc. Japan 52 (4) 877 - 898, October, 2000. https://doi.org/10.2969/jmsj/05240877

Information

Published: October, 2000
First available in Project Euclid: 10 June 2008

zbMATH: 0995.53047
MathSciNet: MR1774634
Digital Object Identifier: 10.2969/jmsj/05240877

Subjects:
Primary: 53A10
Secondary: 53C42 , 58E20

Keywords: Harmonic Maps , normal Gauss maps , representation formula , Surfaces in the hyperbolic 3-space

Rights: Copyright © 2000 Mathematical Society of Japan

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Vol.52 • No. 4 • October, 2000
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