A Characteristic Property of the Grassmann Manifold Representing the Lines of a Projective Space

The Grassmann Space of a Planar Space

“…, then Property I implies Property II, and Melone and Olanda [2], have shown that this characterizes the Grassmann space G(S) of a projective space P = (S, L, P). Their theorem can be rephrased as follows.…”

On a characterization of the Grassmann graphs

“…Much attention has been paid to the problem of characterization of the Grassmann graphs (or, in terms of finite geometry, the Grassmann manifolds as a class of incidence structures satisfying certain conditions), see [1,2,4,5,6,17,35,37,48,51,52,53,54]. The strongest result in this direction was obtained by Metsch in [38], where he showed that the Grassmann graph J q (n, D), D ≥ 3, can be uniquely determined as a distance-regular graph by its intersection numbers unless one of the following few cases holds:…”

A Characterization of Grassmann Spaces of Index h of a Projective Space

“…There are several results concerning the combinatorial characterization of Grassmann spaces, see, for example, the papers of Cooperstein [6], Cohen [4], Bichara and Tallini ( [2] and [3]) and Melone and Olanda [7]. In particular, in 1982/83, Bichara and Tallini in [2] and [3] characterized Grassmann spaces of index h of a projective space P, involving intersection properties of the two disjoint families and T of maximal subspaces of Gr(h, P).…”

“…In 1984 Melone and Olanda in [7] characterized the Grassmann space Gr(1, P) of the lines of a projective space P using only one family of maximal subspaces. More precisely, they point out that for every maximal subspace S ∈ and for every point p / ∈ S, every subspace of passing through p intersects S at a unique point and these points trace out a line formed by all points of S collinear with p.…”