Geodesic
Affine Cylinders
Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 697-700.

Voir la notice de l'article provenant de la source Math-Net.Ru

An affine cylinder is defined as a surface for which all affine normals are parallel to the same plane. It is proved that a complete strictly convex affine cylinder is a translation surface whose line of translation is a parabola.
Keywords: affine cylinder, complete strictly convex affine cylinder, translation surface
Mots-clés : affine normal, Hessian matrix. 
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V. N. Kokarev. Affine Cylinders. Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 697-700. http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a5/

[1] P. A. Shirokov, A. P. Shirokov, Affinnaya differentsialnaya geometriya, Fizmatgiz, M., 1959 | MR | Zbl

[2] E. Calabi, “Complete affine hyperspheres. I”, Sympos. Math., 10 (1972), 19–38 | MR | Zbl

[3] S. T. Cheng, S. T. Yau, “Complete affine hypersurfaces. Part I. The completeness of affine metrics”, Comm. Pure Appl. Math., 39:6 (1986), 839–866 | DOI | MR | Zbl

[4] A. V. Pogorelov, Mnogomernoe uravnenie Monzha–Ampera $\det\|z_{ij}\|=\varphi(z_1,\dots,z_n,z, x_1,\dots,x_n)$, Nauka, M., 1988 | MR | Zbl