王新民,许志才.双曲空间中旋转对称的极小超曲面[J].数学研究及应用,1991,11(3):383~386 |
双曲空间中旋转对称的极小超曲面 |
Minimal Hypersurface of Revolution in Hyperbolic Space Hn |
投稿时间:1989-10-24 |
DOI:10.3770/j.issn:1000-341X.1991.03.015 |
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中文摘要: |
本文给出了双曲空间Hn中旋转对称的极小超曲面的微分方程,对这类超曲面进行了分类,它们是Hn中的超平面或广义悬链面,而每个广义悬链面被夹在两个平行的超平面之间,且以这两个超平面为渐近平面. |
英文摘要: |
Let M be a rotational minimal hypersurface in the hyperbolic space Hn. In this paper, we give differential equation of the generating curve γ in the fundamental domain H+2, and obtain the following clossification theorem.Theorem The rotational minimal hypersurfaces in the hyperbolic space Hn muse be hyperplane or generalized catenoids. Moreover, each generalized cat-enoid is bounded between two parallel hyperplanes and is asymptotic them. |
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