The center map of a centroaffine ruled surface

Received: 12.VI.2017, Accepted: 21.IX.2017

Abstract. We determine a nondegenerate centroaffine ruled surface such that the image of its center map lies on a plane containing the origin. A centroaffine minimal surface such that the image of the center map lies on a plane not containing the origin is also exhibited.
Moreover, we study a nondegenerate centroaffine ruled surface such that the image of its center map lies on a curve, and illustrate a one parameter family of such surfaces having the same center map.
Keywords: centroaffine surface, ruled surface, center map

Mathematics Subject Classification (2010): 53A15, 53A05

Authors:

Atsushi Fujioka, Department of Mathematics, Kansai University, Suita 564-8680, Japan

Hitoshi Furuhata (Corresponding author), Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan