PONTRJAGIN FORMS, CHERN-SIMONS CLASSES, CODAZZI TRANSFORMATIONS, AND AFFINE HYPERSURFACES

We show that the primary and secondary characteristic classes vanish i n the context of affine differential geometry. This gives rise to obst ructions to realizing a conformal class of metrics on a manifold eithe r as the first or as the second fundamental form of an affine immersio n. (C) 1998 Elsevier Science B.V.