Curves on ruled surfaces under infinitesimal bending

Abstract

Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the bending of curves on the cylinder, the hyperbolic paraboloid and the helicoid are considered and appropriate bending fields are found. Some examples are graphically presented.

Keywords

• infinitesimal bending
• curve
• ruled surface
• cylinder
• hyperbolic paraboloid
• helicoid