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

Author Salvador Gigena

(Received August 30, 2000, revised May 14, 2001)
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 $\det(\partial_{ij}f)=\pm1$.

2000 Mathematics Subject Classification. Primary 53A15. Secondary 35J60.

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