设x:Mn→Sn+1是球面Sn+1中的一个定向超曲面,其共形高斯映照G=(H,Hx+en+1):Mn→R1n+3是Möbius变换群下的一个不变量,其中H,en+1 分别是超曲面的平均曲率和单位法向量场.本文研究了S4中具有调和共形高斯映照的超曲面,分类了具有调和共形高斯映照和常Möbius数量曲率的超曲面,给出了具有调和共形高斯 映照但不是Willmore超曲面的例子.
Abstract
Let x: Mn→Sn+1 be an oriented hypersurface in Sn+1, the conformal Gauss map G=(H,Hx+en+1): Mn→R1n+3 1 is invariant under Möbius transformations of Sn+1, where H, en+1 are the mean curvature, the global unit normal vector field of x, respectively.In this paper, we study the oriented hypersurface x: M3 → S4 with harmonic conformal Gauss map, and we classify the hypersurfaces in S4 with constant Möbius scalar curvature under Möbius transformation group, which gives some examples of hypersurfaces with harmonic conformal Gauss map, but not Willmore hypersurfaces.
关键词
Mö /
bius变换群 /
共形高斯映照 /
Willmore超曲面
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Key words
Mö /
bius transformation group /
conformal Gauss map /
Willmore hypersurfaces
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参考文献
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脚注
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基金
国家自然青年基金资助项目(10801006, 1097055)
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