HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

doi:10.1016/S0252-9602(11)60300-7

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 1091-1102.doi: 10.1016/S0252-9602(11)60300-7

HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

苏变萍, 舒世昌*, Yi Annie Han

Department of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China|Department of Mathematics, Xianyang Normal University, Xianyang 712000, China

收稿日期:2008-12-16 出版日期:2011-05-20 发布日期:2011-05-20
基金资助:
Project supported by NSF of Shaanxi Province (SJ08A31), NSF of Shaanxi Educational Committee (2008JK484; 2010JK642) and Talent Fund of Xi'an University of Architecture and Technology.

HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

SU Bian-Ping, SHU Shi-Chang*, Yi Annie Han

Department of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China|Department of Mathematics, Xianyang Normal University, Xianyang 712000, China

Received:2008-12-16 Online:2011-05-20 Published:2011-05-20
Supported by:
Project supported by NSF of Shaanxi Province (SJ08A31), NSF of Shaanxi Educational Committee (2008JK484; 2010JK642) and Talent Fund of Xi'an University of Architecture and Technology.

摘要/Abstract

摘要：

Let Mⁿbe an n-dimensional complete connected and oriented hypersurface in a hyperbolic space Hⁿ⁺¹(c) with non-zero constant mean curvature H and two distinct principal curvatures. In this paper, we show that (1) if the multiplicities of the two distinct
principal curvatures are greater than 1, then Mⁿ is isometric to the Riemannian product S^k(r)×H^^n-k(-1/(r^2+ρ²)), where r>0 and 1<k<n-1; (2) if H²>-c and one of the two distinct principal curvatures is simple, then Mⁿis isometric to the Riemannian product Sⁿ^-1(r)×H¹(-1/(r²+ρ²)) or S¹(r)×Hⁿ^-1(-1/(r²+ρ²)), r>0, if one of the following conditions is satisfied (i) S≤(n-1)t²₂+c²t^-2₂ on Mⁿ or (ii) S≥(n-1)t²₁+c²t^-2₁ on Mⁿor (iii) (n-1)t²₂+c²t^-2₂≤S≤ (n-1)t²₁+c²t^-2₁ on Mⁿ, where t₁ and t₂ are the positive real roots of (1.5).

关键词: hypersurface, hyperbolic space, scalar curvature, mean curvature, principal curvature

Abstract:

Key words: hypersurface, hyperbolic space, scalar curvature, mean curvature, principal curvature

中图分类号:

53C42

苏变萍, 舒世昌, Yi Annie Han. HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE[J]. 数学物理学报(英文版), 2011, 31(3): 1091-1102.

SU Bian-Ping, SHU Shi-Chang, Yi Annie Han. HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE[J]. Acta mathematica scientia,Series B, 2011, 31(3): 1091-1102.

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HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A HYPERBOLIC SPACE

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