On Higher Dimensional Kaluza-Klein Theories

We present a new method for the study of general higher dimensional Kaluza-Klein theories. Our new approach is based on the Riemannian adapted connection and on a theory of adapted tensor fields in the ambient space. We obtain, in a covariant form, the fully general 4D equations of motion in a (4 + n)D general gauge Kaluza-Klein space. This enables us to classify the geodesics of the (4 + n)D space and to show that the induced motions in the 4D space bring more information than motions from both the 4D general relativity and the 4D Lorentz force equations. Finally, we note that all the previous studies on higher dimensional Kaluza-Klein theories are particular cases of the general case considered in the present paper.