A QUALITATIVE STUDY OF KALUZA-KLEIN THEOR IES

The models derived from the Kaluza-Klein type theories in arbitrary di mension n, after reduction to four dimensions, give Einstein's equatio ns coupled to scalar fields. We use the dynamical system analysis to s tudy in two main cases the vacuum solutions of these effective models when the four-dimensional metric is the Robertson-Walker one: first we take the curvature of the internal and external spaces as null; secon dly, we suppose a non vanishing curvature of the internal space, manta ining null the curvature of the external space. Finally, we analyse a third case, where both curvatures are zero, but an external field is a dded to the equations that describe the dynamics of the Universe.