On the geometry of Grassmannian equivalent connections

Abstract

AbstractWe study the geometry ofn-Grassmannian equivalent connections, that is linear connections without torsion admitting the same equation ofn-dimensional totally geodesic submanifolds. We introduce then-Grassmannian structure as a distinguished distribution on the Grassmann bundle, and then compute then-Grassmannian invariants, recovering forn= 1 the projective invariants of Thomas.