Abstract
The following hypothesis is investigated. A parapolar space _ has a class M of maximal singular subspaces of finite projective rank, covering all lines, and having the property that, for any non-incident pair (x, M) ∈ (P,M), x⊥ ∩ M is empty or is a PG(d) for a fixed positive integer dPolar spaces have this property and if d > 2, that is the only possibility. Otherwise. If d > 2, _ is a polar space, and if d = 2, _ is a homomorphic image of a half-spin geometry. But when d = 1, _ is a Grassmannian of k-spaces of a possibly infinite-dimensional vector space, or is a space in which each line lies in a unique member of M and has tightly controlled point-residues. No example is known that would realize this last case.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
