Isometries of Grassmann spaces, II

Surjective Isometries on Grassmann Spaces

Let H be a complex Hilbert space, n a given positive integer and let Pn(H) be the set of all projections on H with rank n. Under the condition dimH ≥ 4n, we describe the surjective isometries of Pn(H) with respect to the gap metric (the metric induced by the operator norm).

Transformations of Grassmann spaces

This is a current version of a part of the book “Transformations of Grassmann spaces”. We study transformations of Grassmann spaces preserving certain geometrical constructions (related with buildings). The next part will be devoted to Grassmann spaces associated with polar spaces.

Embeddings of Affine Grassmann Spaces

In this paper we prove that if a Grassmann space Δ = GrA(m,h,K) of the h–subspaces of an affine space A = AG(m,K) has an embedding e into a projective space PG(n,K′) over a skew–field K′, and e satisfies two suitable conditions (α) and (β), then K and K′ are isomorphic fields and Δ is, up to projections, an affine Grassmannian. Mathematics Subject Classification (2000). 51A45; 51M35.

On Isometries of Euclidean Spaces

Spaces of Pencils, Grassmann Spaces, and Generalized Veronese Spaces

In this paper we construct several examples of partial linear spaces. First, we define two algebraic structures, namely the spaces of k-pencils and Grassmann spaces for vector spaces over an arbitrary field. Then we introduce the notion of generalized Veronese spaces following the definition presented in the paper [8] by Naumowicz and Prażmowski. For all spaces defined, we state the conditions ...