Almost para-quaternionic structures on smooth manifolds of dimension 2 n are equivalent to almost Grassmannian structures of type (2, n ). We remind the equivalence and exhibit some interrelations between subjects that were previously studied independently from the para-quaternionic and the Grassmannian point of view. In particular, we relate the respective normalization conditions, distinguished curves, and twistor constructions.

中文翻译：

---

对四元数和格拉斯曼几何之间的相互作用

维数为 2 n 的光滑流形上的几乎对四元数结构等效于类型 (2, n ) 的几乎格拉斯曼结构。我们提醒等价性并展示先前独立于对四元数和格拉斯曼观点研究的主题之间的一些相互关系。特别是，我们将各自的归一化条件、不同的曲线和扭曲器结构联系起来。