Yayli, Yusuf; Saracoglu, Semra On developable ruled surfaces. (English) Zbl 1259.53004 Algebras Groups Geom. 28, No. 2, 165-184 (2011). The authors study ruled surfaces obtained from the motion of the Frenet frame \(\{T,N,B\}\) of one curve \(\alpha\) along a second curve \(\beta\). The ruled surfaces in question have \(\beta\) as director line and the direction \(X\) of a ruling is fixed in the moving Frenet frame of \(\alpha\). Particular emphasis is put on the cases where \(X\) is one of the Frenet basis vectors. After providing criteria for the developability of these ruled surfaces, the authors compute certain differential invariants like harmonic curvature, angle of pitch, length of pitch and the distribution parameter. Reviewer: Hans-Peter Schröcker (Innsbruck) Cited in 1 Document MSC: 53A04 Curves in Euclidean and related spaces 53A05 Surfaces in Euclidean and related spaces 53A17 Differential geometric aspects in kinematics Keywords:ruled surface; Frenet frame; developable surface; harmonic curvature; pitch; distribution parameter PDFBibTeX XMLCite \textit{Y. Yayli} and \textit{S. Saracoglu}, Algebras Groups Geom. 28, No. 2, 165--184 (2011; Zbl 1259.53004) Full Text: arXiv