## Tohoku Mathematical Journal 2002 December SECOND SERIES VOL. 54, NO. 4

 Tohoku Math. J. 54 (2002), 495-512

Title ON AFFINE HYPERSURFACES WITH PARALLEL SECOND FUNDAMENTAL FORM

Abstract. We investigate the classification problem of hypersurfaces with affine normal parallel second fundamental (cubic) form. A new method of approaching the solution to this problem is here presented; it consists in showing and using the equivalence of the mentioned problem with the classification of a certain class of solutions to the equation of Monge-Ampere type $\det(\partial_{ij}f)=\pm1$.