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On one class of holonomy groups in pseudo-Riemannian geometry

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posted on 2016-06-13, 09:11 authored by Alexey BolsinovAlexey 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.

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School

  • Science

Department

  • Mathematical Sciences

Citation

BOLSINOV, A.V. and TSONEV, D., 2014. On one class of holonomy groups in pseudo-Riemannian geometry.arXiv:1107.2361v2 [math.DG]

Publisher

arXiv.org

Version

  • SMUR (Submitted Manuscript Under Review)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2014

Notes

This pre-print was submitted to arXiv on 31st January 2014. The paper was later revised and published as a journal article, the details are: BOLSINOV, A.V. and TSONEV, D., 2014. On a new class of holonomy groups in pseudo-Riemannian geometry. Journal of Differential Geometry, 97 (3), pp.377-394

Language

  • en

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