EULER FORMS IN KALUZA-KLEIN THEORIES

A 2k-dimensional Euler form dimensionally continued to n = 2k + 3 dimensions is analysed in the framework of a higher-dimensional theory. The dimensional reduction is performed by averaging the n-dimensional equations of motion over the internal coordinates. The effective 4-equations are shown to contain the standard Einstein-Yang-Mills term with vanishing cosmological constant, a massless scalar field and some additional fields of a non-standard type. It is argued that the internal symmetries of the type of the direct product of groups cannot be realized by choosing the internal space in the form of the group manifold. A relation between the gravitational and SO(d + 1) gauge coupling constants is obtained that slightly differs from the well-known Weinberg formula.