Interactions between para-quaternionic and Grassmannian geometry

Abstract

Almost para-quaternionic structures on smooth manifolds of dimension $2n$ 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.

Article reorganized, some issues clarified (e.g. the normalization), some added (e.g. distinguished curves), some suppressed (e.g. appendix). 21 pages