Surjections on grassmannians preserving pairs of elements with bounded distance - Lim, M.H. (Elsevier, 2010)
Let m and k be two fixed positive integers such that m > k >= 2. Let V be a left vector space over a division ring with dimension at least m + k + 1. Let G(m) (V) be the Grassmannian consisting of all m-dimensional subspaces of V. We characterize surjective mappings T from g, (V) onto itself such that for any A, B in 9,,(V), the distance between A and B is not greater than k if and only if the distance between T(A) and T(B) is not greater than k. (C) 2009 Elsevier Inc. All rights reserved.