A NEW CHARACTERIZATION OF COMPLETE LINEAR WEINGARTEN HYPERSURFACES IN REAL SPACE FORMS

被引：23
|
作者：
Aquino, Cicero P. [1 ]
de Lima, Henrique F. [2 ]
Velasquez, Marco A. L. [2 ]
机构：
[1] Univ Fed Piaui, Dept Matemat, BR-64049550 Teresina, Piaui, Brazil
[2] Univ Fed Campina Grande, Dept Matemat & Estat, BR-58429970 Campina Grande, Paraiba, Brazil
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2013年 / 261卷 / 01期
关键词：
space forms; linear Weingarten hypersurfaces; totally umbilical hypersurfaces; Clifford torus; circular cylinder; hyperbolic cylinder; CONSTANT SCALAR CURVATURE; RIEMANNIAN MANIFOLDS; MEAN-CURVATURE;
D O I：
10.2140/pjm.2013.261.33
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We apply the Hopf's strong maximum principle in order to obtain a suitable characterization of the complete linear Weingarten hypersurfaces immersed in a real space form Q(c)(n+1) of constant sectional curvature c. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a Clifford torus, if c = 1, a circular cylinder, if c = 0, or a hyperbolic cylinder, if c = -1.
引用
收藏
页码：33 / 43
页数：11
相关论文
共 50 条
  • [21] Linear Weingarten hypersurfaces in locally symmetric manifolds
    Chao, Xiaoli
    Wang, Peijun
    HOKKAIDO MATHEMATICAL JOURNAL, 2017, 46 (01) : 29 - 40
  • [22] Complete Hypersurfaces with Two Distinct Principal Curvatures in a Space Form
    Gomes, Jose N.
    de Lima, Henrique F.
    Velasquez, Marco Antonio L.
    RESULTS IN MATHEMATICS, 2015, 67 (3-4) : 457 - 470
  • [23] On the rigidity of hypersurfaces into space forms
    Barros, Abdenago
    Aquino, Cicero
    de Lima, Henrique
    ANNALI DI MATEMATICA PURA ED APPLICATA, 2014, 193 (03) : 689 - 698
  • [24] LINEAR WEINGARTEN HYPERSURFACES IN A UNIT SPHERE
    Li, Haizhong
    Suh, Young Jin
    Wei, Guoxin
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2009, 46 (02) : 321 - 329
  • [25] On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds
    Aquino, Cicero P.
    de Lima, Henrique F.
    dos Santos, Fabio R.
    Velasquez, Marco Antonio L.
    COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2015, 56 (04): : 515 - 529
  • [26] STABILITY OF GENERALIZED LINEAR WEINGARTEN HYPERSURFACES IMMERSED IN THE EUCLIDEAN SPACE
    da Silva, Jonathan F.
    de Lima, Henrique F.
    Velasquez, Marco Antonio L.
    PUBLICACIONS MATEMATIQUES, 2018, 62 (01) : 95 - 111
  • [27] LINEAR WEINGARTEN HYPERSURFACES WITH BOUNDED MEAN CURVATURE IN THE HYPERBOLIC SPACE
    Aquino, Cicero P.
    De Lima, Henrique F.
    Velasquez, Marco Antonio L.
    GLASGOW MATHEMATICAL JOURNAL, 2015, 57 (03) : 653 - 663
  • [28] Strongly Stable Linear Weingarten Hypersurfaces Immersed in the Hyperbolic Space
    Henrique F. de. Lima
    Antonio F. de. Sousa
    Marco Antonio L. Velásquez
    Mediterranean Journal of Mathematics, 2016, 13 : 2147 - 2160
  • [29] Linear Weingarten hypersurfaces in locally symmetric manifolds
    Chao, Xiaoli
    Wang, Peijun
    BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 2014, 19 (02): : 50 - 59
  • [30] COMPLETE WEINGARTEN HYPERSURFACES SATISFYING AN OKUMURA TYPE INEQUALITY
    De Lima, Eudes L.
    De Lima, Henrique F.
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2020, 109 (01) : 81 - 92
12345