Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature

Details Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature

2010-03-12

arxiv.org/abs/1003.2574v3

Ann Glob Anal Geom (2011) 39:99-105

Mathematics

Differential Geometry

7 pages; Dedicated to Dmitri Vladimirovich Alekseevsky at the occasion of his 70th birthday

Scientific paper

10.1007/s10455-010-9234-0

The holonomy group $G$ of a pseudo-quaternionic-K\"ahlerian manifold of signature $(4r,4s)$ with non-zero scalar curvature is contained in $\Sp(1)\cdot\Sp(r,s)$ and it contains $\Sp(1)$. It is proved that either $G$ is irreducible, or $s=r$ and $G$ preserves an isotropic subspace of dimension $4r$, in the last case, there are only two possibilities for the connected component of the identity of such $G$. This gives the classification of possible connected holonomy groups of pseudo-quaternionic-K\"ahlerian manifolds of non-zero scalar curvature.

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