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

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概要

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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.

• 東北大学の論文

著者

• Aiyama Reiko

  Institute Of Mathematics University Of Tsukuba

• Akutagawa Kazuo

  Department of Mathematics, Shizuoka University

• Akutagawa Kazuo

  Department Of Mathematics Faculty Of Science Kyushu University

関連論文

• Complete space-like hypersurfaces with constant mean curvature in a Lorentz space form of dimension 4.
• Minimal maps between the hyperbolic discs and generalized Gauss maps ofmaximal surfaces in the anti-de sitter 3-space
• Kenmotsu type representation formula for surfaces with prescribed mean curvature in the 3-sphere
• The generalized Gauss map of a space-like submanifold with parallel mean curvature vector in a pseudo-Euclidean space
• The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space
• Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space
• A note on spacelike hypersurfaces with prescribed mean curvature in a spatially closed globally static Lorentzian manifold
• Notes on the relative Yamabe invariant

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