Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 52, Number 1 (2000), 95-105.
Kenmotsu type representation formula for surfaces with prescribed mean curvature in the $3$-sphere
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.
Tohoku Math. J. (2), Volume 52, Number 1 (2000), 95-105.
First available in Project Euclid: 3 May 2007
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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