Weakly irreducible subgroups of \(\text{Sp}(1,n+1)\). (English) Zbl 1212.53071

Bezvitnaya, Natalia I.

Arch. Math., Brno 44, No. 5, 341-352 (2008).

Summary: Connected weakly irreducible not irreducible subgroups of \(\text{Sp}(1,n+1)\subset \text{SO}(4,4n+4)\) that satisfy a certain additional condition are classified. This is used to classify connected holonomy groups of pseudo-hyper-Kählerian manifolds of index 4.

MSC:

53C29	Issues of holonomy in differential geometry
53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics

Keywords:

pseudo-hyper-Kählerian manifold of index 4; weakly irreducible holonomy group