The Grassmann-like Manifold of Centered Planes

被引：3
作者：
Belova, O. O. [1 ]
机构：
[1] Immanuel Kant Baltic Fed Univ, Kaliningrad 236041, Russia
来源：
MATHEMATICAL NOTES | 2018年 / 104卷 / 5-6期
关键词：
Cartan's exterior form method; Grassmann manifold; Norden's normalization; average connection;
D O I：
10.1134/S000143461811024X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Connections associated with the Grassmann-like manifold of centered planes in the multidimensional projective space are studied. A geometric interpretation of these connections in terms of maps and translations of equipping planes is given. An intrinsic analog of Norden's strong normalization of the manifold under consideration is constructed.
引用
收藏
页码：789 / 798
页数：10
相关论文
共 22 条
  • [1] Akivis M. A., 2007, ELIE CARTAN
  • [2] Baralic D, 2011, TEACH MATH-SERB, V14, P147
  • [3] Belova O. O., 2007, DIFFERENTIAL GEOMETR, V38, P6
  • [4] Belova O. O., 2009, DIFFER GEOM MNOGOOBR, V40, P18
  • [5] BORISENKO AA, 1991, USP MAT NAUK, V46, P41
  • [6] Chakmazyan A. V., 1978, PROBLEMS IN GEOMETRY, P55
  • [7] CHERN SS, 1961, COMPLEX MANIFOLDS
  • [8] On the Grassmann space representing the lines of an affine space
    Di Gennaro, Roberta
    Dentice, Eva Ferrara
    Lo Re, Pia Maria
    [J]. DISCRETE MATHEMATICS, 2012, 312 (03) : 699 - 704
  • [9] Evtushik L.E., 1979, Differential Geometric Structures on Manifolds
  • [10] Finikov S. P., 1948, Cartans Method of External Forms in Differential Geometry
123