Holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Annals of Global Analysis and Geometry |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Pseudo-quaternionic-Kählerian manifold; Non-zero scalar curvature; Holonomy group; Holonomy algebra; Curvature tensor; Symmetric space |
| Description | 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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