  Multidimensional theories still remain attractive from the point of view of
better understanding of fundamental interactions. In this paper we consider a
six - dimensional Kaluza -- Klein type model at the classical level. We derive
static spherically symmetric solutions to the multidimensional Einstein
equations. They are fundamentally different from four - dimensional
Schwarzschild solutions: they are horizon free and the presence of massless
dilaton field has the same dynamical effect as the existence of additional
massive matter in the system. Then we analyse the motion of test particles in
such spherically symmetric configurations. The emphasis is put on some
observable quantities like redshifts. It is suggested that strange features of
emission lines from active galactic nuclei as well as quasar - galaxy
associations may in fact be manifestations of multidimensionality of our world.
