Surface Family Pair with Bertrand Pair as Mutual Curvature Lines in Three-Dimensional Lie Group

Abstract

This paper is on deducing the necessary and sufficient conditions of a surface family pair with a Bertrand pair as mutual curvature lines in three-dimensional Lie group G. As a result, the consequence for the ruled surface family pair is also extrapolated. Meanwhile, examples are specified to show the surface family with common Bertrand geodesic curves.

Keywords

• Serret–Frenet formulae
• Bertrand pair
• marching-scale functions