Abstract
A model problem is solved for a six-dimensional spacetime where ordinary four-space is flat and the two extra dimensions have the geometry of a two-sphere. The geometry is driven by coupled Yang-Mills and Higgs fields. The equations of motion are derived from a geometric theory of the canonical gravitation-Yang-Mills-Higgs fields. The constant radius of the two-sphere is determined. If certain reasonable values are taken for various arbitrary constants in the theory, the radius is of the order of the Planck length and an exact value for the coupling constant of the Yang-Mills field is obtained.