Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces. I
Generalized rotational hypersurfaces of constant mean curvature in the Euclidean spaces. I
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DOI：
10.4310/jdg/1214436924
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发表时间：
1987-11
影响因子：
2.5
通讯作者：
W. Hsiang
中科院分区：
文献类型：
--
作者：
W. Hsiang
在欧氏（n +1）-空间MncEn +1中给定超曲面的各种基本局部微分几何不变量中，平均曲率（即第二基本形式的迹）无疑是最简单的具有重要几何意义的数值不变量之一，即“面积”的第一变分。因此，E n+1中常平均曲率的完备超曲面自然构成了一个简单的整体几何对象的好家族，当然值得特别关注。特别是，这些闭空间可以看作是“肥皂泡”的自然推广，自Euler和Monge以来，欧氏空间中的广义肥皂泡问题一直吸引着微分几何学家的注意。本文是E n+1中广义旋转型常平均曲率超曲面的系统研究的第二部分，是前一篇同名文章的延续.
Among various basic local differential geometric invariants of a given hypersurface in the euclidean (n + l)-space, M n c E n+ι , the mean curvature, i.e. the trace of the second fundamental form, is certainly one of the simplest numerical invariants with important geometric meaning, namely, the first variation of "area". Therefore, complete hypersurfaces of constant mean curvatures in E n+1 naturally constitute a nice family of simple global geometric objects that certainly deserve special attention. Especially, those closed ones can be considered as natural generalizations of "soap bubbles" and the problem of such generalized soap bubbles in the euclidean spaces has been attracting the attention of differential geometers since Euler and Monge. This paper is the second part of a systematic study of hypersurfaces of constant mean curvatures in E n+ι which are of generalized rotational types, succeeding a previous paper with the same title.