Geometric structures on finite- and infinite-dimensional Grassmannians

Abstract

In this paper, we study the Grassmannian of n-dimensional subspaces of a 2n-dimensional vector space and its infinite-dimensional analogues. Such a Grassmannian can be endowed with two binary relations (adjacent and distant), with pencils (lines of the Grassmann space) and with so-called Z-reguli. We analyse the interdependencies among these different structures.

Correction of two typos

References in corpus (5)

• On bijections that preserve complementarity of subspaces
• The Connected Components of the Projective Line over a Ring
• On distant-isomorphisms of projective lines
• Extending the Concept of Chain Geometry
• Diameter preserving surjections in the geometry of matrices

Cited by in corpus (1)

• Projective Ring Lines and Their Generalisations