Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature
| Autoři | |
|---|---|
| Rok publikování | 2011 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Annals of Global Analysis and Geometry |
| Fakulta / Pracoviště MU | |
| Citace | |
| Obor | Obecná matematika |
| Klíčová slova | Pseudo-quaternionic-Kählerian manifold; Non-zero scalar curvature; Holonomy group; Holonomy algebra; Curvature tensor; Symmetric space |
| Popis | 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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