## Tohoku Mathematical Journal

### Kenmotsu type representation formula for surfaces with prescribed mean curvature in the $3$-sphere

#### Abstract

Our primary object of this paper is to give a representation formula for a surface with prescribed mean curvature in the (metric) 3-sphere by means of a single component of the generalized Gauss map. For a CMC (constant mean curvature) surface, we derive another representation formula by means of the adjusted Gauss map. These formulas are spherical versions of the Kenmotsu representation formula for surfaces in the Euclidean 3-space. Spin versions of them are obtained as well.

#### Article information

Source
Tohoku Math. J. (2), Volume 52, Number 1 (2000), 95-105.

Dates
First available in Project Euclid: 3 May 2007

https://projecteuclid.org/euclid.tmj/1178224660

Digital Object Identifier
doi:10.2748/tmj/1178224660

Mathematical Reviews number (MathSciNet)
MR1740545

Zentralblatt MATH identifier
1008.53012

#### Citation

Aiyama, Reiko; Akutagawa, Kazuo. Kenmotsu type representation formula for surfaces with prescribed mean curvature in the $3$-sphere. Tohoku Math. J. (2) 52 (2000), no. 1, 95--105. doi:10.2748/tmj/1178224660. https://projecteuclid.org/euclid.tmj/1178224660

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