We study the geometry of n-Grassmannian equivalent connections, that is linear connections without torsion admitting the same equation of n-dimensional totally geodesic submanifolds. We introduce the n-Grassmannian structure as a distinguished distribution on the Grassmann bundle, and then compute the n-Grassmannian invariants, recovering for n = 1 the projective invariants of Thomas. © de Gruyter 2008.
Manno, G. (2008). On the geometry of Grassmannian equivalent connections. ADVANCES IN GEOMETRY, 8(3), 329-342 [10.1515/ADVGEOM.2008.021].
On the geometry of Grassmannian equivalent connections
MANNO, GIOVANNI
2008
Abstract
We study the geometry of n-Grassmannian equivalent connections, that is linear connections without torsion admitting the same equation of n-dimensional totally geodesic submanifolds. We introduce the n-Grassmannian structure as a distinguished distribution on the Grassmann bundle, and then compute the n-Grassmannian invariants, recovering for n = 1 the projective invariants of Thomas. © de Gruyter 2008.
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