Tohoku Mathematical Journal

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

Reiko Aiyama and Kazuo Akutagawa

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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

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

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53C27: Spin and Spin$^c$ geometry


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.

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