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
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Key words
the conformal second fundamental form /
self-conjugate linear operators /
Lorentzian hypersurfaces
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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.
[2] Li H. Z., Liu H. L., Wang C. P., et al., Möbius isoparametric hypersurfaces in Sn+1 with two distinct principal curvatures, Acta Math. Sinica, English Series, 2002, 18: 437–446.
[3] Li H. Z., Wang C. P., Surfaces with vanishing Moebius form in Sn, Acta Math. Sinica, English Series, 2003, 19: 671–678.
[4] Liu H. L., Wang C. P., Zhao G. S., Möbius isotropic submanifolds in Sn, Tohoku Math. J., 2001, 53: 553–569.
[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.
[8] Wang C. P., Canonical equiaffine hypersurfaces in Rn+1, Math. Z., 1993, 214: 579–592.
[9] Wang C. P., Moebius geometry of submanifolds in Sn, Manuscripta Math., 1998, 96: 517–535.
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脚注
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