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.
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页码：810 / 815
页数：5
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