Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space
type: Item
instance of: scholarly article
title: Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space
zbMATH Open document ID: 0995.53047
author: Reiko Aiyama
author: Kazuo Akutagawa
published in: Journal of the Mathematical Society of Japan
publication date: 2002-10-23T00:00:00Z
review text: It is well known that the Weierstrass-Enneper representation formula plays an important role in the theory of minimal surfaces in Euclidean space \(E^3\). In 1979, K. Kenmotsu gave a representation formula for surfaces with non-zero constant mean curvature in Euclidean space \(E^3\). In this paper, the authors obtain a hyperbolic version of the result due to Kenmotsu. That is, they derive a representation formula for surfaces in the hyperbolic space \(H^3(-c)\) with constant mean curvature \(0<H<c\). It is necessary to point out that \textit{R. Bryant} [Astérisque 154-155, 321-347 (1988; Zbl 0635.53047)] gave the representation formula for surfaces in the hyperbolic space \(H^3(-c)\) with constant mean curvature \(c\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1553007
zbMATH Keywords: minimal surfaces in Euclidean space
zbMATH Keywords: surfaces in the hyperbolic space
zbMATH Keywords: constant mean curvature
zbMATH Keywords: representation formula
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05240877
OpenAlex ID: W2019314037
DOI: 10.2969/JMSJ/05240877
description: scientific article; zbMATH DE number 1553007