On one class of holonomy groups in pseudo-Riemannian geometry

Alexey Bolsinov; Dragomir Tsonev

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arXiv · 1107.2361

On one class of holonomy groups in pseudo-Riemannian geometry

Alexey Bolsinov·Dragomir Tsonev

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Abstract

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.

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Alexey Bolsinov, Dragomir Tsonev. 2014-01-31. On one class of holonomy groups in pseudo-Riemannian geometry. https://arxiv.org/abs/1107.2361

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