Note on the holonomy groups of pseudo-Riemannian manifolds

被引：0
|
作者：
A. S. Galaev
机构：
[1] Masaryk University,
来源：
Mathematical Notes | 2013年 / 93卷
关键词：
holonomy algebra; pseudo-Riemannian manifolds; linear connection; Levi-Cività connection; curvature tensor; Lorentzian manifold;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For an arbitrary subalgebra h ⊂ so(r, s) a polynomial pseudo-Riemannian metric of signature (r + 2, s + 2) is constructed, the holonomy algebra of this metric contains h as a subalgebra. This result shows the essential distinction between the holonomy algebras of pseudo-Riemannian manifolds of index greater than or equal to 2 and the holonomy algebras of Riemannian and Lorentzian manifolds.
引用
收藏
页码：810 / 815
页数：5
相关论文
共 50 条
  • [41] INVARIANT COEFFICIENT OPERATORS ON PSEUDO-RIEMANNIAN MANIFOLDS
    BABBITT, D
    JOURNAL OF MATHEMATICS AND MECHANICS, 1966, 15 (04): : 643 - &
  • [42] PSEUDO-RIEMANNIAN MANIFOLDS WITH TOTALLY GEODESIC BISECTORS
    BEEM, JK
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A205 - A205
  • [43] Indefinite Kasparov Modules and Pseudo-Riemannian Manifolds
    Koen van den Dungen
    Adam Rennie
    Annales Henri Poincaré, 2016, 17 : 3255 - 3286
  • [44] Pseudo-Riemannian manifolds with recurrent spinor fields
    Galaev, A. S.
    SIBERIAN MATHEMATICAL JOURNAL, 2013, 54 (04) : 604 - 613
  • [45] FLAT PSEUDO-RIEMANNIAN STRUCTURES OF COMPACT MANIFOLDS
    FURNESS, P
    FEDIDA, E
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1978, 286 (03): : 169 - 171
  • [46] Pseudo-Riemannian manifolds with simple Jacobi operators
    Bonome, A
    Castro, R
    García-Río, E
    Hervella, L
    Vázquez-Lorenzo, R
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2002, 54 (04) : 847 - 875
  • [47] ON THE BIHARMONICITY OF VECTOR FIELDS ON PSEUDO-RIEMANNIAN MANIFOLDS
    Alem, Amina
    Kacimi, Bouazza
    Ozkan, Mustafa
    HONAM MATHEMATICAL JOURNAL, 2023, 45 (02): : 300 - 315
  • [48] PSEUDO-RIEMANNIAN MANIFOLDS WITH TOTALLY GEODESIC BISECTORS
    BEEM, JK
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 49 (01) : 212 - 215
  • [49] SOLITON EXCITATIONS IN TERMS OF PSEUDO-RIEMANNIAN MANIFOLDS
    WIATROWSKI, G
    PHYSICA STATUS SOLIDI B-BASIC RESEARCH, 1985, 129 (02): : 607 - 614
  • [50] Parallel pure spinors on pseudo-Riemannian manifolds
    Kath, I
    GEOMETRY AND TOPOLOGY OF SUBMANIFOLDS X: DIFFERENTIAL GEOMETRY IN HONOR OF PROF S.S. CHERN, 2000, : 87 - 103
12345