Abstract :
A method is proposed for constructing the geometries of the non-Abelian Kaluza–Klein theories of generalized monopoles in arbitrary dimensions. These represent a natural generalization of the Euclidean Taub-NUT space, regarded as the appropriate background of the Dirac magnetic monopole. A recent theory of induced representations governing the isometries of the Euclidean Taub-NUT space is combined with usual geometrical methods obtaining a conjecture in which the potentials of the generalized monopoles can be written down without to solve explicitly the Yang–Mills equations. Moreover, in this way one finds that apart from the monopole models, which are of a space-like type, there exists a new type of time-like models that cannot be interpreted as monopoles. The space-like models are studied pointing out that their monopole fields strength are particular solutions of the Yang–Mills equations with central symmetry, producing the standard flux of 4π through the two-dimensional spheres surrounding the monopole. Examples are given of manifolds with Einstein metrics carrying image monopoles.
