Journal of Differential Geometry

On a new class of holonomy groups in pseudo-Riemannian geometry

Alexey Bolsinov and Dragomir Tsonev

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Abstract

We describe a new class of holonomy groups on pseudo-Riemannian manifolds. Namely, let $g$ be a nondegenerate bilinear form on a vector space $V$, and $L : V \to V$ a $g$-symmetric operator. Then the identity component of the centraliser of $L$ in $\mathrm{SO}(g)$ is a holonomy group for a suitable Levi-Civita connection.

Article information

Source
J. Differential Geom., Volume 97, Number 3 (2014), 377-394.

Dates
First available in Project Euclid: 22 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1406033974

Digital Object Identifier
doi:10.4310/jdg/1406033974

Mathematical Reviews number (MathSciNet)
MR3233515

Zentralblatt MATH identifier
1296.53101

Citation

Bolsinov, Alexey; Tsonev, Dragomir. On a new class of holonomy groups in pseudo-Riemannian geometry. J. Differential Geom. 97 (2014), no. 3, 377--394. doi:10.4310/jdg/1406033974. https://projecteuclid.org/euclid.jdg/1406033974


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