双曲空间中的共形平坦极小超曲面(英文)

Conformally Flat Minimal Hypersurfaces in a Hyperbolic Space

英文关键词:minimal submanifolds  conformal flatness  hyperbolic space.

中文摘要:

      本文证明了双曲空间中的共形平坦极小超曲面必为旋转超曲面或由一些旋转超曲面片用全测地超曲面片粘合而成．将这结果与王新民及许志才的一个已发表定理相组合，推广了Ｂｌａｉｒ关于推广悬链面的一个定理．

英文摘要:

      In this paper it is proved that all the conformally flat minimal hypersurfaces in a hyperbolic space are either rotational hypersurfaces or glued by some such pieces via totally geodesic ones. Combining this result with a previous theorem of Wang Xinmin and Xu Zhicai, We generalize a theorem of Blair about a generalization of catenoid.