Centroaffine space curves with constant curvatures and homogeneous surfaces
The present paper contributes to the differential geometry of the three dimensional centroaffine space, that is, the study of objects invariant by affine transformations in \({\mathbb R}^3\) fixing the origin. The authors give a classification of curves with constant centroaffine curvatures which leads to four types of solutions. As in the Euclidean situation, these curves are centroaffine and homogeneous, that means, they are orbits of one parameter subgroups of \(\mathrm{GL}(3,\mathbb R)\). Furthermore, in three cases, the authors find a centroaffine homogeneous surface carrying the curve.
scientific article; zbMATH DE number 6054111