On distinguished local coordinates for locally homogeneous affine surfaces

被引：0
|
作者：
Brozos-Vazquez, M. [1 ]
Garcia-Rio, E. [2 ]
Gilkey, P. [3 ]
机构：
[1] Univ A Coruna, Differential Geometry & Its Applicat Res Grp, Escola Politecn Super, Ferrol 15403, Spain
[2] Univ Santiago de Compostela, Fac Math, Santiago De Compostela 15782, Spain
[3] Univ Oregon, Dept Math, Eugene, OR 97403 USA
来源：
MONATSHEFTE FUR MATHEMATIK | 2020年 / 192卷 / 01期
关键词：
Affine surface; Locally homogeneous; Local forms; Affine Killing equations; SYMMETRIC RICCI TENSOR; CONNECTIONS; CLASSIFICATION; MANIFOLDS;
D O I：
10.1007/s00605-020-01382-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a new short self-contained proof of the result of Opozda (Differ Geom Appl 21:173-198, 2004) classifying the locally homogeneous torsion free affine surfaces and the extension to the case of surfaces with torsion due to Arias-Marco and Kowalski (Monatsh Math 153:1-18, 2008). Our approach rests on a direct analysis of the affine Killing equations and is quite different than the approaches taken previously in the literature.
引用
收藏
页码：65 / 74
页数：10
相关论文
共 50 条
  • [1] On distinguished local coordinates for locally homogeneous affine surfaces
    M. Brozos-Vázquez
    E. García-Río
    P. Gilkey
    Monatshefte für Mathematik, 2020, 192 : 65 - 74
  • [2] Spaces of locally homogeneous affine surfaces
    Brozos-Vazquez, Miguel
    Garcia-Rio, Eduardo
    Gilkey, Peter
    REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2020, 114 (01)
  • [3] Spaces of locally homogeneous affine surfaces
    M. Brozos-Vázquez
    E. García-Río
    P. Gilkey
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020, 114
  • [4] Locally homogeneous affine connections on compact surfaces
    Opozda, B
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (09) : 2713 - 2721
  • [5] A classification of locally homogeneous affine connections on compact surfaces
    Adolfo Guillot
    Antonia Sánchez Godinez
    Annals of Global Analysis and Geometry, 2014, 46 : 335 - 349
  • [6] A classification of locally homogeneous affine connections on compact surfaces
    Guillot, Adolfo
    Sanchez Godinez, Antonia
    ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2014, 46 (04) : 335 - 349
  • [7] On curvature homogeneous and locally homogeneous affine connections
    Opozda, B
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (06) : 1889 - 1893
  • [8] AFFINE LOCALLY SYMMETRIC SURFACES
    JELONEK, W
    GEOMETRIAE DEDICATA, 1992, 44 (02) : 189 - 221
  • [9] Homogeneous affine surfaces: Moduli spaces
    Brozos-Vazquez, M.
    Garcia-Rio, E.
    Gilkey, P.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 444 (02) : 1155 - 1184
  • [10] The Geometry of Locally Symmetric Affine Surfaces
    D'Ascanio, D.
    Gilkey, P.
    Pisani, P.
    VIETNAM JOURNAL OF MATHEMATICS, 2019, 47 (01) : 5 - 21
12345