VOLUME-FORMS AND MINIMAL ACTION PRINCIPLES IN AFFINE MANIFOLDS

Through the analysis of volume-forms in differentiable manifolds, it i s shown that the usual way of defining minimal action principles for f ield theory on curved space-times is not appropriate on non-riemannian manifolds. An alternative approach, based in a new volume-form, is pr oposed and confronted with the standard one. The new volume element is explicitly used in the study of Einstein-Cartan theory of gravity and its relation to string theory, in connection with some recent results on the subject.