MASSLESS SCALAR FIELDS IN NON-ABELIAN KALUZA-KLEIN THEORY

We investigate the presence of massless scalar fields in a Kaluza-Klei n theory based on a dimensionally continued Euler-form action. We show that massless scalar fields exist provided that the internal space is a direct product of two irreducible manifolds. The condition of a van ishing effective four-dimensional cosmological constant and the presen ce of a graviton, gauge fields and massless scalar fields can be satis fied if both irreducible manifolds have odd dimensions and the sum of these dimensions is equal to the dimension of the Euler form.