Tokyo Journal of Mathematics

Surfaces and Fronts with Harmonic-mean Curvature One in Hyperbolic Three-space

Masatoshi KOKUBU

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Abstract

We show a global representation formula for a certain kind of Weingarten surface in hyperbolic three-space, which is based on the formula due to Gálvez, Martínez and Milán. As an application of the representation formula, we also investigate surfaces with harmonic-mean curvature one (HMC-1 surfaces). We allow them to have certain kinds of singularities, and discuss some global properties.

Article information

Source
Tokyo J. Math., Volume 32, Number 1 (2009), 177-200.

Dates
First available in Project Euclid: 7 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1249648416

Digital Object Identifier
doi:10.3836/tjm/1249648416

Mathematical Reviews number (MathSciNet)
MR2541163

Zentralblatt MATH identifier
1211.53079

Subjects
Primary: 53C45: Global surface theory (convex surfaces à la A. D. Aleksandrov)
Secondary: 53A35: Non-Euclidean differential geometry

Citation

KOKUBU, Masatoshi. Surfaces and Fronts with Harmonic-mean Curvature One in Hyperbolic Three-space. Tokyo J. Math. 32 (2009), no. 1, 177--200. doi:10.3836/tjm/1249648416. https://projecteuclid.org/euclid.tjm/1249648416


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References

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