On invariants of curves in centro-affine geometry
The paper deals with global \(n\)-dimensional centro-affine geometry of curves. Four global types of curves are defined using the limit of centro-affine arc length to the endpoints of the definition interval. The authors present a system of centro-affine curvature functions which is shown to be complete. In contrast to a paper of \textit{R. B. Gardner} and \textit{G. R. Wilkens} [Bull. Belg. Math. Soc. Simon Stevin 4, No. 3, 379--401 (1997; Zbl 0936.53010)], the authors give explicit formulae of curvatures in terms of the centro affine invariant parameter. Furthermore, an existence theorem is proved.
scientific article; zbMATH DE number 5010266