Rotation Hypersurfaces in Spaces of Constant Curvature
Rotation Hypersurfaces in Spaces of Constant Curvature
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DOI：
10.1007/978-3-642-25588-5_17
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发表时间：
1983-02
影响因子：
1.3
通讯作者：
M. Carmo;M. Dajczer
中科院分区：
文献类型：
--
作者：
M. Carmo;M. Dajczer
定义了常曲率空间中的旋转超曲面，并计算了它们的主曲率。这种超曲面的局部特征，与尺寸大于2，给出的主曲率。研究了双曲空间中具有常平均曲率的旋转超曲面的一些特殊情形。特别是，它表明，众所周知的共轭之间的螺旋面和悬链面在欧几里德三空间自然延伸到双曲三空间H3;在后者的情况下，悬链面是三种不同的类型和明确的对应关系。证明了H3中存在一族单连通的、完备的、嵌入的、非完全测地稳定极小曲面。
Rotation hypersurfaces in spaces of constant curvature are defined and their principal curvatures are computed. A local characterization of such hypersurfaces, with dimensions greater than two, is given in terms of principal curvatures. Some special cases of rotation hypersurfaces, with constant mean curvature, in hyperbolic space are studied. In particular, it is shown that the well-known conjugation between the helicoid and the catenoid in euclidean three-space extends naturally to hyperbolic three-space H3; in the latter case, catenoids are of three different types and the explicit correspondence is given. It is also shown that there exists a family of simply-connected, complete, embedded, nontotally geodesic stable minimal surfaces in H3.