摘要
本文研究Ｓ~３中完备正则具常中曲率的旋转曲面，通过求解二阶非线性常微分方程组，构造出Ｓ~３中单参数族常中曲率的完备曲面。特别地，在极小曲面情形，证明了此单参数族的曲面中含有可数无穷多个互不相同的紧致无边极小曲面，同时还含有非可数无穷个完备非紧致的极小曲面。
This paper investigates the complete and regular rotation surfaces with constantmean curvature in S￣3.Through solving an order two nonlinear ordinary equation system,constructsa 1-parameter family of complete rotation surfaces with constant mean curvature in S￣3.For the min-imal case,we show that there are numerable indefinitive compact minimal surfaces without bound-ary in this 1-parameter family of surfaces and all the other innumerable indefinitive surfaces in this1-parameter family of surfaces are complete noncompact minimal surfaces.
出处
《郑州大学学报（自然科学版）》
CAS
1994年第4期1-6,共6页
Journal of Zhengzhou University (Natural Science)
基金
河南省自然科学基金资助项目
关键词
常中曲率
极小曲面
完备曲面
旋转曲面
constant mean curvature
minimal surfaces
compact
complete
