Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2020, Vol. 49(1): 73-82
研究论文
非平坦洛伦兹空间型中 $\eta$-双调和超曲面的分类
Classification of $\eta$-biharmonic Hypersurfaces in Nonflat Lorentz Space Forms

独力, 张娟
DU Li*, ZHANG Juan**

重庆理工大学理学院, 重庆, 400054
School of Science, Chongqing University of Technology, Chongqing, 400054, P. R. China

收稿日期: 2018-09-26
出版日期: 2020-03-25
2020, Vol. 49(1): 73-82
DOI: 10.11845/sxjz.2018081b


PDF
[187 KB]
44
下载
106
浏览

引用导出
0
    /   /   推荐

摘要 本文对非平坦洛伦兹空间型中形状算子极小多项式的阶数至多为2的$\eta$-双调和超曲面进行了完全分类.
关键词 洛伦兹空间型超曲面形状算子极小多项式    
Abstract:In this paper, we classify completely the $\eta$-biharmonic hypersurface in a nonflat Lorentz space form with the minimal polynomial of the shape operator of degree $\leq 2$.
Key wordsLorentz space form    hypersurfaces    shape operator    minimal polynomial
PACS:  O186.16  
通讯作者: E-mail: *duli820210@cqut.edu.cn; **zhangjuan_1225@163.com   
[1] Abe N., Koike N. and Yamaguchi S., Congruence theorems for proper semi-Riemannian hypersurfaces in a real space form, Yokohama Math. [J]., 1987, 35(1/2): 123-136.
[2] Alías L.J., Ferrández A. and Lucas P., Hypersurfaces in the non-flat Lorentzian space forms with a characteristic eigenvector field, J. Geom., 1995, 52(1/2): 10-24.
[3] Arvanitoyeorgos A., Defever F. and Kaimakamis G., Hypersurfaces of $E^4_s$ with proper mean curvature vector, J. Math. Soc. Japan, 2007, 59(3): 797-809.
[4] Arvanitoyeorgos A., Defever F., Kaimakamis G. and Papantoniou V.J., Biharmonic Lorentz hypersurfaces in $E^{4}_{1}$, Pacific J. Math., 2007, 229(2): 293-305.
[5] Arvanitoyeorgos, A. and Kaimakamis, G., Hypersurfaces of type $M^3_2$ in $E^4_2$ with proper mean curvature vector, J. Geom. Phys., 2013, 63: 99-106.
[6] Chen B.-Y.,Null 2-type surfaces in $E^3$ are circular cylinders, Kodai Math. [J]., 1988, 11(2): 295-299.
[7] Chen B.-Y.,Pseudo-Riemannian Geometry, $\delta$-Invariants and Applications, Hackensack, NJ: World Scientific, 2011.
[8] Chen, B.-Y. and Ishikawa, S., Biharmonic surfaces in pseudo-Euclidean spaces, Mem. Fac. Sci. Kyushu Univ. Ser. A, 1991, 45(2): 323-347.
[9] Chen, B.-Y. and Ishikawa, S., Biharmonic pseudo-Riemannian submanifolds in pseudo-Euclidean spaces, Kyushu J. Math., 1998, 52(1): 167-185.
[10] Defever F.,Hypersurfaces of $\bar{\mathbb{E}}^4$ satisfying $\Delta\vec{H}=\lambda\vec{H}$, Michigan Math. [J]., 1997, 44(2): 355-363.
[11] Defever F., Kaimakamis G. and Papantoniou V., Biharmonic hypersurfaces of the 4-dimensional semi-Euclidean space $\mathbb{E}^{4}_{s}$, J. Math. Anal. Appl., 2006, 315(1): 276-286.
[12] Du, L., Classification of $\eta$-biharmonic surfaces in non-flat Lorentz space forms, Mediterr. J. Math., 2018, 15(5): Art. 203, 14 pp.
[13] Du, L. and Liu, J.C., Classification of proper biharmonic hypersurfaces in Lorentz space forms, Chinese Ann. Math. Ser. A, 2018, 39(1): 63-76 (in Chinese).
[14] Du L., Zhang J. and Xie X., Hypersurfaces satisfying $\tau_2(\phi)=\eta\tau(\phi)$ in pseudo-Riemannian space forms, Math. Phys. Anal. Geom.,2017, 20(2): Art. 17, 23 pp.
[15] Ferrández, A. and Lucas, P., On surfaces in the 3-dimensional Lorentz-Minkowski space, Pacific J. Math., 1992, 152(1): 93-100.
[16] Ferrández, A. and Lucas, P., Classifying hypersurfaces in the Lorentz-Minkowski space with a characteristic eigenvector, Tokyo J. Math., 1992, 15(2): 451-459.
[17] Garray O.J.,A classification of certain 3-dimensional conformally flat Euclidean hypersurfaces, Pacific J. Math., 1994, 162(1): 13-25.
[18] Inoguchi J.,Biminimal submanifolds in contact 3-manifolds, Balkan J. Geom. Appl., 2007, 12(1): 56-67.
[19] Jiang G.Y.,2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A, 1986, 7(4): 389-402 (in Chinese).
[20] Liu, J.C. and Du, L., Classification of proper biharmonic hypersurfaces in pseudo-Riemannian space forms, Differential Geom. Appl., 2015, 41: 110-122.
[21] Liu J.C., Du L. and Zhang J., Minimality on biharmonic space-like submanifolds in pseudo-Riemannian space forms, J. Geom. Phys., 2015, 92: 69-77.
[22] Liu, J.C. and Yang, C., Hypersurfaces in $\mathbb{E}^{n+1}_s$ satisfying $\Delta\vec{H}=\lambda\vec{H}$ with at most two distinct principal curvatures, J. Math. Anal. Appl., 2017, 451(1): 14-33.
[23] Magid M.A.,Lorentzian isoparametric hypersurfaces, Pacific J. Math., 1985, 118(1): 165-197.
[24] O'Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Pure and Applied Mathematics, Book 103, New York: Academic Press, 1983.
[25] Ou Y.-L.,Biharmonic hypersurfaces in Riemannian manifolds, Pacific J. Math., 2010, 248(1): 217-232.
[26] Sasahara T.,Quasi-minimal Lagrangian surfaces whose mean curvature vectors are eigenvectors, Demonstratio Math., 2005, 38(1): 185-196.
[27] Sasahara T.,Biharmonic submanifolds in nonflat Lorentz 3-space forms, Bull. Aust. Math. Soc., 2012, 85(3): 422-432.
[28] Takahashi T.,Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan, 1966, 18: 380-385.
[1] 林燕斌. 四维时空中两个不同主曲率类时共形齐性超曲面的分类[J]. 数学进展, 2019, 48(5): 607-619.
[2] 刘珊, 贺群. Randers空间中的常旗曲率旋转超曲面[J]. 数学进展, 2018, 47(1): 109-116.
[3] 朱鹏. 空间形式中具有常平均曲率的超曲面的特征值估计[J]. 数学进展, 2017, 46(1): 133-140.
[4] 胡传峰, 姬秀. F-相对极值超曲面的Bernstein性质[J]. 数学进展, 2016, 45(1): 143-152.
[5] 姬秀,胡传峰. \mbox{\boldmath $\mathbb{R}^{5}$}\ 中的Laguerre等参超曲面[J]. 数学进展, 2015, 44(1): 117-127.
[6] 舒世昌;朱天民;. 单位球面中紧致超曲面的曲率结构与拓扑性质[J]. 数学进展, 2007, 36(6): 728-736.
[7] 安天庆. 正定型超曲面上双曲闭特征的Maslov型指标的迭代公式(英文)[J]. 数学进展, 2005, 34(3): 355-360.
[8] 舒世昌,刘三阳. 局部对称流形中具常平均曲率的完备超曲面(英文)[J]. 数学进展, 2004, 33(5): 563-569.
[9] 李光汉,吴传喜. 球面中具有常平均曲率超曲面的谱特征(英文)[J]. 数学进展, 2004, 33(5): 575-580.
[10] 张廷枋. S~(n+1)中Mebius形式平行的超曲面[J]. 数学进展, 2003, 32(2): 230-238.
[11] 张学山. 全拟脐子流形中的稳定积分流(英文)[J]. 数学进展, 2001, 30(5): 435-442.
[12] 成庆明. S~4(1)中具有常拟Gauss-Kronecker曲率的超曲面[J]. 数学进展, 1993, 22(2): 125-132.
Viewed
Full text


Abstract

Cited

  Discussed   
首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录


© 2015-2017 北京大学图书馆 .