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 8 条
  • [1] Hano J(1956)On the holonomy group of linear connections Nagoya Math. J. 10 97-100
  • [2] Ozeki H(1955)Sur les groupes d’holonomie homogénes des variétésà connexion affine et des variétés riemanniennes Bull. Soc. Math. France 83 279-330
  • [3] Berger M(1999)Classification of irreducible holonomies of torsion-free affine connections Ann. of Math. (2) 150 77-149
  • [4] Merkulov S(1968)Riemannian spaces with exceptional holonomy groups Funktsional. Anal. i Prilozhen. 2 1-10
  • [5] Schwachhöfer L(2011)QR-submanifolds and Riemannian metrics with holonomy Mat. Zametki 90 781-784
  • [6] Alekseevskii D V(2007)On the classification of Lorentzian holonomy groups J. Differential Geom. 76 423-484
  • [7] Egorov D V(undefined)undefined undefined undefined undefined-undefined
  • [8] Leistner T(undefined)undefined undefined undefined undefined-undefined
1