Journal of the Mathematical Society of Japan

Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space

Reiko AIYAMA and Kazuo AKUTAGAWA

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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.

Article information

Source
J. Math. Soc. Japan, Volume 52, Number 4 (2000), 877-898.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107115

Digital Object Identifier
doi:10.2969/jmsj/05240877

Mathematical Reviews number (MathSciNet)
MR1774634

Zentralblatt MATH identifier
0995.53047

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 58E20: Harmonic maps [See also 53C43], etc.

Keywords
Surfaces in the hyperbolic 3-space normal Gauss maps harmonic maps representation formula

Citation

AIYAMA, Reiko; AKUTAGAWA, Kazuo. Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space. J. Math. Soc. Japan 52 (2000), no. 4, 877--898. doi:10.2969/jmsj/05240877. https://projecteuclid.org/euclid.jmsj/1213107115


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