Killing vectors, constraints and conserved charges in Kaluza-Klein theories

The traditional Abelian and non-Abelian Kaluza-Klein ansaetze are analysed from a geometrical point of view using a Bochner-Yano type theorem for geodesic Killing vector fields. It is shown how the presence of Killing vectors in the ansatz gives rise to constraints on the Yang-Mills fields and the curvature. The conserved Komar quantities associated with these Killing vectors are computed and compared with the corresponding ADM charges. A crucial difference between them in the presence of external fields is pointed out. (author)