摘要设f :Mm → R1m+1是无脐点类空超曲面,则在Mm上可以定义四个基本的共形不变量:共形度量g,共形1-形式C,共形第二基本形式B,共形Blaschke张量A.如果存在光滑函数λ和常数μ,使得A+μB=λg,则称Mm是拟迷向类空超曲面.本文不仅构造了拟迷向类空超曲面的例子,同时在相差R1m+1的一个共形变换下,本文还完全分类了拟迷向类空超曲面. | | 服务 | | | 加入引用管理器 | | E-mail Alert | | RSS | 收稿日期: 2019-05-29 | | 基金资助:国家自然科学基金资助项目(11571037)
| 作者简介: 姬秀,E-mail:jixiu1106@163.com;李同柱,E-mail:litz@bit.edu.cn |
[1] Cahen M., Kerbrat Y., Domaines symmétriques des quadriques projectives, J. Math. Pure Appl., 1983, 62:327-348. [2] Cheng Q. M., Li X. X., Qi X. R., A classification of hypersurfaces with parallel para-Blaschke tensor in Sm+1, Int. J. Math., 2010, 21:297-316. [3] Guo Z., Fang J. B., Lin L. M., Hypersurfaces with isotropic Blaschke tensor, J. Math. Soc. Japan, 2011, 4:1155-1186. [4] Guo Z., Li H., Wang C. P., The Möbius characterizations of Willmore tori and Veronese submanifolds in unit sphere, Pacific J. Math., 2009, 241:227-242. [5] Fang J. B., Zhang K., Hypersurfaces with isotropic para-Blaschke tensor, Acta Math. Sinica, English Series, 2014, 30(7):1195-1209. [6] 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. [7] Ji X., Li T. Z., Sun H. F., Para-Blaschke isoparametric spacelike hypersurfaces in Lorentzian space forms, Houston Journal of Mathematics, 2019, 45(3):685-706. [8] Li F. J., Fang J. B., Liang L., Surfaces with isotropic Blaschke tensor in S3, Acta Math. Sinica, English series, 2015, 31(5):863-878. [9] Li H. Z., Wang C. P., Möbius geometry of hypersurfaces with constant mean curvature and scalar curvature, Manuscripta Math., 2003, 112:1-13. [10] Li T. Z., Nie C. X., Spacelike Dupin hypersurfaces in Lorentzian space forms, Journal of the Mathematical Society of Japan, 2018, 70:463-480. [11] Li T. Z., Nie C. X., Regular Blaschke para-umbilical hypersurfaces in the conformal space Qsn, arXiv:1512.04158, 2015[math.DG]. [12] Li X. X., Song H. R., On the regular space-like hypersurfaces in the de Sitter space R1m+1 with parallel Blaschke tensors, J. of Math., 2016, 36:1183-1200. [13] Li X. X., Song H. R., Regular space-like hypersurfaces in R1m+1 with parallel para-Blaschke tensors, Acta Math. Sin. Engl. Ser., 2017, 33(10):1361-1381. [14] Li X. X., Zhang F. Y., A classification of immersed hypersurfaces in spheres with parallel Blaschke tensors, Tohoku Math. J., 2006, 58:581-597. [15] Nie C. X., Blaschke isoparametric hypersurfaces in the conformal space Q1n+1 I, Acta Math. Sinica, English Series, 2015, 31(11):1751-1758. [16] Nie C. X., Conformal geometry of hypersurfaces and surfaces in Lorentz space forms, Doctoral dissertation, Perking University, 2006. [17] Nie C. X., Li T. Z., He Y. J., et al., Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space, Science China Math., 2010, 53:953-965. [18] Nie C. X., Wu C. X., Space-like hypersurfaces with parallel conformal second fundamental forms in the conformal space, Acta Math. Sinica, Chinese Series, 2008, 51(4):685-692. [19] O'Neil B., Semi-Riemannian Geometry, Academic Press, New York, 1983. [20] Wang C. P., Möbius geometry of submanifolds in Sn, Manuscripta Math., 1998, 96:517-534.
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[1] | 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[J]. Acta Mathematica Sinica, English Series, 2015, 58(6): 897-910. | [2] | 聂昌雄, 田大平, 吴传喜. 共形空间中具有平行的共形第二基本形式的I型类时超曲面的分类[J]. Acta Mathematica Sinica, English Series, 2011, 54(1): 125-136. | [3] | 徐海峰. 方程Δg-aKg=0无正函数解的充分条件[J]. Acta Mathematica Sinica, English Series, 2010, 53(5): 945-952. | [4] | 聂昌雄;吴传喜;. 共形空间中平行的共形第二基本形式的类空超曲面[J]. Acta Mathematica Sinica, English Series, 2008, 51(4): 685-692. | [5] | 李海中. H~3(c)中常平均曲率曲面的稳定性[J]. Acta Mathematica Sinica, English Series, 1991, 34(5): 599-603. |
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