The curve whose curvature is a function
F. Dillen, "The classification of hypersurfaces of an Euclidean space with parallel higher order fundamental form", Math. Z. 203 (1999) 635--643.
Elsa Abbena, Simon Salamon and Alfred Gray, "Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition", 2006, Chapman and Hall/CRC.