2016/11/04 by Anton S. Galaev
Mathematics · Physics and Astronomy · #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1088/0264-9381/31/13/135007
published as Classical and Quantum Gravity 31 (2014), no. 13, 135007, 13 pp · 9 pages; this is an extanded version of a part from arXiv:1110.1998 that was published
arxiv created 2016/11/04 · arxiv updated 2016/11/08
It is explained how to find the de~Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold.