Ruled surface family with common special curve

Abstract

In this paper, we investigate the problem of the construction of a ruled surface family passing through the striction curve (c) of a ruled surface φ. We first define ruled surface family with common striction curve (c). Using the geodesic Frenet frame {e,t,g} of the ruled surface φ, we present sufficient conditions for that striction curve to be geodesic, line of curvature and asymptotic curve. Finally, we give some examples to show ruled surfaces with common geodesic, line of curvature and asymptotic curve.