## Tohoku Mathematical Journal

### 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-Ampère type $\det(\pa_{ij}f)=\pm1$.

#### Article information

Source
Tohoku Math. J. (2), Volume 54, Number 4 (2002), 495-512.

Dates
First available in Project Euclid: 11 April 2005

https://projecteuclid.org/euclid.tmj/1113247647

Digital Object Identifier
doi:10.2748/tmj/1113247647

Mathematical Reviews number (MathSciNet)
MR1936266

Zentralblatt MATH identifier
1033.53009

#### Citation

Gigena, Salvador. On affine hypersurfaces with parallel second fundamental form. Tohoku Math. J. (2) 54 (2002), no. 4, 495--512. doi:10.2748/tmj/1113247647. https://projecteuclid.org/euclid.tmj/1113247647

#### References

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