2002 Volume 54 Issue 4 Pages 495-512
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-Ampère type $\det(\partial_{ij}f)=\pm1$.
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