Rotational hypersurfaces of space forms with constant scalar curvature
Rotational hypersurfaces of space forms with constant scalar curvature
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DOI：
10.1007/bf02568434
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发表时间：
1990-12
影响因子：
0.6
通讯作者：
M. L. Leite
中科院分区：
文献类型：
--
作者：
M. L. Leite
设M是空间形式中具有常数量曲率的完备旋转超曲面。本文在Rn和Hn的情形下对这类超曲面进行了分类，确定了这三种空间中Sin的容许值，并根据S的值给出了这类超曲面的几何描述。在Sn的情况下，我们找到了具有常数S ∈（n−2/n−1，1）的嵌入超曲面的例子，它们不是等距于球面的乘积。
LetMbe a complete rotational hypersurface of a space form with constant scalar curvatureS. In this paper we classify these hypersurfaces in the cases ofRnandHn, determine the admissible values ofSin each of the three spaces and give a geometrical description of the hypersurfaces according to the values ofS. In the case ofSnwe find examples of embedded hypersurfaces with constantS∈(n−2/n−1, 1), which are not isometric to product of spheres.