Rn中具有平行Laguerre形式的超曲面

钟定兴, 张祖锦, 陶凌阳

数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 851-862.

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数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 851-862. DOI: 10.12386/A2014sxxb0079
论文

Rn中具有平行Laguerre形式的超曲面

    钟定兴, 张祖锦, 陶凌阳
作者信息 +

The Hypersurfaces with Parallel Laguerre Form in Rn

    Ding Xing ZHONG, Zu Jin ZHANG, Ling Yang TAO
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文章历史 +

摘要

xM→Rn是Rn中定向无脐超曲面,主曲率非零,那么在∪Rn的Laguerre变换群下超曲面的四个Laguerre不变量是Laguerre不变度量g,Laguerre第二基本形式B,Laguerre形式C和Laguerre张量L.本文研究Laguerre形式C平行与Laguerre形式C 为零之间的关系.

Abstract

Let x: M → Rn be an umbilical free oriented hypersurface with non-zero principal curvatures, four basic Laguerre invariants under the Laguerre transformation group are the Laguerre metric g, the Laguerre second fundamental form B, the Laguerre form C and the Laguerre tensor L. In this paper, we study the relationships between parallel Laguerre form and vanishing metric Laguerre form.

关键词

Laguerre 变换群 / Laguerre 形式 / Laguerre 超曲面

Key words

Laguerre transformation group / Laguerre form / Laguerre hypersurface

引用本文

导出引用
钟定兴, 张祖锦, 陶凌阳. Rn中具有平行Laguerre形式的超曲面. 数学学报, 2014, 57(5): 851-862 https://doi.org/10.12386/A2014sxxb0079
Ding Xing ZHONG, Zu Jin ZHANG, Ling Yang TAO. The Hypersurfaces with Parallel Laguerre Form in Rn. Acta Mathematica Sinica, Chinese Series, 2014, 57(5): 851-862 https://doi.org/10.12386/A2014sxxb0079

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(20122BAB201014,20132BAB211007)及江西省教育厅科技项目(GJJ13658,GJJ13659)

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