The Homogeneous Geometries of Real Hyperbolic Space

被引：0
|
作者：
Marco Castrillón López
Pedro Martínez Gadea
Andrew Swann
机构：
[1] Universidad Complutense de Madrid,ICMAT (CSIC
[2] Facultad de Ciencias Matemáticas,UAM
[3] Instituto de Física Fundamenta,UC3M
[4] lCSIC,UCM), Departamento de Geometría y Topología
[5] Aarhus University,Department of Mathematics
[6] University of Southern Denmark,CP3
来源：
Mediterranean Journal of Mathematics | 2013年 / 10卷
关键词：
Primary 53C30; Secondary 57S25; 58H15; Real hyperbolic space; homogeneous structure; holonomy;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components.
引用
收藏
页码：1011 / 1022
页数：11
相关论文
共 50 条
  • [1] The Homogeneous Geometries of Real Hyperbolic Space
    Castrillon Lopez, Marco
    Martinez Gadea, Pedro
    Swann, Andrew
    [J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2013, 10 (02) : 1011 - 1022
  • [2] The homogeneous ruled real hypersurface in a complex hyperbolic space
    Kimura, Makoto
    Maeda, Sadahiro
    Tanabe, Hiromasa
    [J]. JOURNAL OF GEOMETRY, 2018, 109 (01)
  • [3] A characterization of the homogeneous minimal ruled real hypersurface in a complex hyperbolic space
    Maeda, Sadahiro
    Adachi, Toshiaki
    Kim, Young Ho
    [J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2009, 61 (01) : 315 - 325
  • [4] The geometry of homogeneous submanifolds of hyperbolic space
    Di Scala, AJ
    Olmos, C
    [J]. MATHEMATISCHE ZEITSCHRIFT, 2001, 237 (01) : 199 - 209
  • [5] The geometry of homogeneous submanifolds of hyperbolic space
    Antonio J. Di Scala
    Carlos Olmos
    [J]. Mathematische Zeitschrift, 2001, 237 : 199 - 209
  • [6] The homogeneous holonomies of complex hyperbolic space
    J. L. Carmona Jiménez
    M. Castrillón López
    [J]. Annals of Global Analysis and Geometry, 2022, 62 : 391 - 411
  • [7] The homogeneous holonomies of complex hyperbolic space
    Carmona Jimenez, J. L.
    Castrillon Lopez, M.
    [J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2022, 62 (02) : 391 - 411
  • [8] HOMOGENEOUS STRUCTURES ON REAL AND COMPLEX HYPERBOLIC SPACES
    Castrillon Lopez, M.
    Gadea, P. M.
    Swann, A. F.
    [J]. ILLINOIS JOURNAL OF MATHEMATICS, 2009, 53 (02) : 561 - 574
  • [9] Real-time animation in hyperbolic, spherical, and product geometries
    Weeks, JR
    [J]. Non-Euclidean Geometries, 2006, 581 : 287 - 305
  • [10] REAL HYPERSURFACES OF A COMPLEX HYPERBOLIC SPACE
    MONTIEL, S
    [J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1985, 37 (03) : 515 - 535
12345