On tangent spaces and external flats to Grassmannians of lines over finite fields Original Research Article

Let image be the Grassmannian of lines of the projective space PG(n,K), K any field. For any point P of image , let image denote the tangent space to image at P. We give a description of image in terms of incident lines of PG(n,K). Also, by using geometric tools and looking at the orbits of cyclic collineation groups, we construct subspaces of maximal dimension missing the Grassmannian image of lines of the finite projective space PG(n,q).