| 摘要: |
| 本文研究了空间形式中关于Willmore超曲面.从2-型旋转超曲面出发,通过计算2-型旋转超曲面的第一基本形式和第二基本形式,运用活动标架的方法,获得了超曲面是极小Willmore超曲面的等价条件,构造了空间形式中一类具有三个不同主曲率的极小Willmore旋转超曲面的新的例子. |
| 关键词: Willmore超曲面 Willmore泛函 旋转超曲面 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:国家自然科学基金资助 (12161092). |
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| THE MINIMAL WILLMORE HYPERSURFACES WITH THREE DIFFERENT PRINCIPAL CURVATURES IN THE SPACE FORM |
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CHEN Rui-feng
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Department of Mathematics, Yunnan Normal University, Kunming 650500, China
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| Abstract: |
| In this paper, we study the Willmore hypersurface in space form. Starting from the 2-type rotational hypersurface, by calculating the first fundamental form and the second fundamental form of the 2-type rotational hypersurface, using the method of moving frame, we obtain the equivalent condition that the hypersurface is a minimal Willmore hypersurface, and construct a new example of a minimal Willmore rotational hypersurface with three different principal curvatures in space form. |
| Key words: Willmore hypersurface Willmore functional Rotation hypersurface |
