On one class of holonomy groups in pseudo-Riemannian geometry

2016-06-13T09:11:28Z (GMT) by Alexey Bolsinov Dragomir Tsonev
We describe a new class of holonomy groups on pseudo-Riemannian manifolds. Namely, we prove the following theorem. Let g be a nondegenerate bilinear form on a vector space V, and L:V -> V a g-symmetric operator. Then the identity component of the centraliser of L in SO(g) is a holonomy group for a suitable Levi-Civita connection.