On tame ρ-quaternionic manifolds

Abstract

We introduce the notion of tame ρ-quaternionic manifold that permits the construction of a finite family of ρ-connections, significant for the geometry involved. This provides, for example, the following:• A new simple global characterisation of flat (complex-)quaternionic manifolds.• A new simple construction of the metric and the corresponding Levi-Civita connection of a quaternionic-Kähler manifold by starting from its twistor space; moreover, our method provides a natural generalization of this correspondence.Also, a new construction of quaternionic manifolds is obtained, and the properties of twistorial harmonic morphisms with one-dimensional fibres from quaternionic-Kähler manifolds are studied.