On some Grassmannians carrying an even Clifford structure

TL;DR

This paper explicitly describes certain non-flat parallel even Clifford structures on various Grassmannians, exploring the role of octonions, especially in low-dimensional cases, to deepen understanding of their geometric properties.

Contribution

It provides explicit descriptions of non-flat parallel even Clifford structures on Grassmannians and examines the role of octonions in these geometric configurations.

Findings

Explicit descriptions of Clifford structures on Grassmannians

Identification of octonion roles in low-dimensional cases

Insights into the geometry of non-flat structures

Abstract

We give an explicit description of the non-flat parallel even Clifford structures of rank 8, 6, 5 on some real, complex and quaternionic Grassmannians, and discuss the r\^ole of the octonions in them, in particular for some low dimensional examples.