On developable ruled surfaces. (English) Zbl 1259.53004

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.


53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
53A17 Differential geometric aspects in kinematics
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