具有平行的共形第二基本形式的类时超曲面

聂昌雄, 于艳梅, 郑立荷

数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 897-910.

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PDF(524 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (6) : 897-910. DOI: 10.12386/A2015sxxb0089
论文

具有平行的共形第二基本形式的类时超曲面

    聂昌雄, 于艳梅, 郑立荷
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Lorentzian Hypersurfaces with Parallel Conformal Second Fundamental Forms

    Chang Xiong NIE, Yan Mei YU, Li He ZHENG
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摘要

在文[Classification of type I time-like Hyperspaces withparallel conformal second fundamental forms in the conformalspace, Acta Mathematica Sinica, Chinese Series, 2011, 54(1): 125-136]中,我们已对共形空间中具有平行的共形第二基本形式的I型类时超曲面作了分类,本文将探讨其他类型的类时超曲面并完全分类共形空间中具有平行的共形第二基本形式的类时超曲面.

Abstract

In [Classification of type I time-like Hyperspaces with parallel conformal second fundamental forms in the conformal space, Acta Mathematica Sinica, Chinese Series, 2011, 54(1): 125–136], we have classified the Type I Lorentzian hypersurfaces with parallel conformal second fundamental forms in the conformal space. In this paper, we study the rest types of Lorentzian hypersurfaces and classify completely Lorentzian Hypersurfaces with parallel conformal second fundamental forms in the conformal space.

关键词

共形第二基本形式 / 自共轭线性算子 / 类时超曲面

Key words

the conformal second fundamental form / self-conjugate linear operators / Lorentzian hypersurfaces

引用本文

导出引用
聂昌雄, 于艳梅, 郑立荷. 具有平行的共形第二基本形式的类时超曲面. 数学学报, 2015, 58(6): 897-910 https://doi.org/10.12386/A2015sxxb0089
Chang Xiong NIE, Yan Mei YU, Li He ZHENG. Lorentzian Hypersurfaces with Parallel Conformal Second Fundamental Forms. Acta Mathematica Sinica, Chinese Series, 2015, 58(6): 897-910 https://doi.org/10.12386/A2015sxxb0089

参考文献

[1] Hu Z. J., Li H. Z., Classification of hypersurfaces with parallel Möbius second fundamental form in Sn+1, Sci. China Ser. A, 2004, 47: 417–430.

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[5] Nie C. X., Wu C. X., Space-Like hyperspaces with parallel conformal second fundamental forms in the conformal space, Acta Mathematica Sinica, Chinese Series, 2008, 51(4): 685–692.

[6] Nie C. X., Li T. Z., He Y. J., et al., Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space, Sci. China Ser. A, 2010, 53(4): 953–965.

[7] Nie C. X., Tan D. X., Wu C. X., Classification of type I time-like hyperspaces with parallel conformal second fundamental forms in the conformal space, Acta Mathematica Sinica, Chinese Series, 2011, 54(1): 125–136.

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