The set G of all m-dimensional subspaces of a 2m-dimensional vector space V is endowed with two relations, complementarity and adjacency. We consider bijections from G onto G' where G' arises from a 2m-dimensional vector space V'. If such a bijection phi and its inverse leave one of the relations from above invariant, then also the other. In case m >= 2 this yields that phi is induced by a semilinear bijection from V or from the dual space of V onto V'. As far as possible, we include also the infinite-dimensional case into our considerations. (c) 2005 Elsevier B.V. All rights reserved.