Interactions between para-quaternionic and Grassmannian geometry

2013/01/22 by Zadnik, Vojtech
#53A40 #53C05 #53C15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1301.5143

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.

Related

• About the geometry of almost para-quaternionic manifolds
• Twistor and Reflector Spaces of Almost Para-Quaternionic Manifolds
• Conformal and Grassmann structures
• GKM actions on almost quaternionic manifolds
• On the Twistor Theory of Almost-Grassmannian Manifolds