Affine Cylinders

V. N. Kokarev

Samara State University

Abstract: 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, affine normal, Hessian matrix.

UDC: 514.754.4

Received: 29.12.2012
Revised: 28.05.2013

DOI: 10.4213/mzm10238

 English version: Mathematical Notes, 2014, 96:5, 686–689

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