Rn上具有三个主曲率的Laguerre等参超曲面

钟定兴, 谢显华, 陈海莲

数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 195-212.

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数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 195-212. DOI: 10.12386/A2015sxxb0021
论文

Rn上具有三个主曲率的Laguerre等参超曲面

    钟定兴1, 谢显华1, 陈海莲2
作者信息 +

Laguerre Isoparametric Hypersurface in Rn with Three Distinct Principal Curvatures

    Ding Xing ZHONG1, Xian Hua XIE1, Hai Lian CHEN2
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摘要

Rn上主曲率非零的定向无脐超曲面x:MRn称为 Laguerre 等参超曲面,如果它的 Laguerre形式C=∑iCiwi=∑iρ-1(Ei(logρ)(r-ri)-Ei(r))wi为零,Laguerre 形状算子 S=ρ-1(S-rid的特征值为常数, 这里ρ2=∑i(r-ri)2,r=r1+r2+…+rn-1/n-1是平均曲率半径,Sx的形状算子, Ei是Laguerre度量g的单位正交标架, wi是对偶标架.本文给出Rn上具有三个互异Laguerre主曲率的Laguerre等参超曲面的分类.

Abstract

An umbilical free oriented hypersurface x:MRn with nonzero princi-pal curvatures is called Laguerre isoparametric hypersurface if its Laguerre form C=∑i Ciwi =∑iρ-1(Ei(logρ)(r-ri)-Ei(r))wi vanishes and Laguerre shape operator S=ρ-1(S-rid has constant eigenvalues. Here ρ2=∑i(r-ri)2,r=r1+r2+…+rn-1/n-1 is the mean curvature radius and S is the shape operator of x, Ei is local orthogonal basis for Laguerre metric g with dual basis wi. In this paper, we classify all Laguerre isoprametric hypersurfaces in Rn with three distinct Laguerre principal curvatures up to Laguerre transformation.

关键词

Laguerre 等参超曲面 / Laguerre 度量 / Laguerre第二基本形式 / Laguerre 张量

Key words

Laguerre isoparametric hypersurface / Laguerre metric / Laguerre second fundamental form / Laguerre tensor

引用本文

导出引用
钟定兴, 谢显华, 陈海莲. Rn上具有三个主曲率的Laguerre等参超曲面. 数学学报, 2015, 58(2): 195-212 https://doi.org/10.12386/A2015sxxb0021
Ding Xing ZHONG, Xian Hua XIE, Hai Lian CHEN. Laguerre Isoparametric Hypersurface in Rn with Three Distinct Principal Curvatures. Acta Mathematica Sinica, Chinese Series, 2015, 58(2): 195-212 https://doi.org/10.12386/A2015sxxb0021

参考文献

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基金

国家自然科学基金资助项目(11361004);江西省自然科学基金(20122BAB201014,20132BAB21107)及江西省科技厅(GJJ13659)资助项目

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