SOME RIGIDITY THEOREMS IN SEMI-RIEMANNIAN WARPED PRODUCTS

被引：12
|
作者：
Colares, Antonio Gervasio [1 ]
De Lima, Henrique Fernandes [2 ]
机构：
[1] Univ Fed Ceara, Dept Math, BR-60455760 Fortaleza, Ceara, Brazil
[2] Univ Fed Campina Grande, Dept Matemat Estat, BR-58109970 Campina Grande, Paraiba, Brazil
来源：
KODAI MATHEMATICAL JOURNAL | 2012年 / 35卷 / 02期
关键词：
Semi-Riemannian manifolds; hyperbolic-type spaces; steady state-type spacetimes; spacelike hypersurfaces; r-th mean curvatures; CONSTANT MEAN-CURVATURE; COMPLETE SPACELIKE HYPERSURFACES; ROBERTSON-WALKER SPACETIMES; SCALAR CURVATURE; UNIQUENESS; MANIFOLDS;
D O I：
10.2996/kmj/1341401051
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the problem of uniqueness of complete hypersurfaces immersed in a semi-Riemannian warped product whose warping function has convex logarithm. By applying a maximum principle at the infinity due to S. T. Yau and supposing a natural comparison inequality between the mean curvature of the hypersurface and that of the slices of the region where the hypersurface is contained, we obtain rigidity theorems in such ambient spaces. Applications to the hyperbolic and the steady state spaces are given.
引用
收藏
页码：268 / 282
页数：15
相关论文
共 50 条
  • [31] TOTALLY UMBILICAL SUBMANIFOLDS IN SOME SEMI-RIEMANNIAN MANIFOLDS
    Ewert-Krzemieniewski, Stanislaw
    COLLOQUIUM MATHEMATICUM, 2010, 119 (02) : 269 - 299
  • [32] SOME PROPERTIES OF LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN MANIFOLDS
    Kumar, Rakesh
    Rani, Rachna
    Nagaich, R. K.
    DEMONSTRATIO MATHEMATICA, 2010, 43 (03) : 691 - 701
  • [33] SOME REMARKS ON THE RIEMANNIAN METRICS ON WARPED PRODUCTS
    PAK, JS
    KANG, TH
    GEOMETRIAE DEDICATA, 1991, 37 (02) : 227 - 232
  • [34] A Simons Type Formula for Spacelike Submanifolds in Semi-Riemannian Warped Product and its Applications
    Lobos, Guillermo A.
    Melara, Mynor
    Santos, Maria R. B.
    RESULTS IN MATHEMATICS, 2024, 79 (08)
  • [35] Foliations of Semi-Riemannian Manifolds
    Lars Schäfer
    Results in Mathematics, 2012, 61 : 97 - 126
  • [36] Semi-Riemannian submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection
    Yucesan, Ahmet
    Yasar, Erol
    COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 27 (04): : 781 - 793
  • [37] Contact Semi-Riemannian Structures in CR Geometry: Some Aspects
    Perrone, Domenico
    AXIOMS, 2019, 8 (01)
  • [38] CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds
    Perdomo, Oscar M.
    MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2012, 15 (01) : 17 - 37
  • [39] Barycentric interpolation on Riemannian and semi-Riemannian spaces
    Pihajoki, Pauli
    Mannerkoski, Matias
    Johansson, Peter H.
    MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 2019, 489 (03) : 4161 - 4169
  • [40] Foliations of Semi-Riemannian Manifolds
    Schaefer, Lars
    RESULTS IN MATHEMATICS, 2012, 61 (1-2) : 97 - 126
12345