3D-Darboux motions in 4-dimensional Euclidean space.
The aim of this paper is to give an easy explicit description of 3-K-contact structures on SO(3)-principal fibre bundles over Wolf quaternionic Kähler manifolds.
We study 3-submersions from a QR-hypersurface of a quaternionic Kähler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kähler manifolds which are not locally hyper-Kähler.
On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.
The aim of this article is to answer a question posed by J. Oprea in his talk at the Workshop "Homotopy and Geometry".