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.

我们引入了驯服的ρ -四元数流形的概念，它允许构建有限的ρ -连接族，这对于所涉及的几何非常重要。例如，这提供了以下内容：

• 平面（复）四元数流形的新的简单全局表征。

• 度量的新简单构造以及四元数-Kähler 流形的相应列维-奇维塔连接，从其扭曲空间开始；此外，我们的方法提供了这种对应关系的自然概括。

此外，还获得了四元流形的新构造，并研究了四元-Kähler 流形中具有一维纤维的扭曲调和态射的性质。