Tohoku Mathematical Journal
2000
March
SECOND SERIES VOL. 52, NO. 1

Tohoku Math. J.
52 (2000), 95-105

Title KENMOTSU TYPE REPRESENTATION FORMULA FOR SURFACES WITH PRESCRIBED MEAN CURVATURE IN THE 3-SPHERE

Author Reiko Aiyama and Kazuo Akutagawa

(Received August 11, 1998, revised May 6, 1999)
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.

1991 Mathematics Subject Classification. Primary 53A10; Secondary 53C42, 58E20.

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