On Geometry Of Some Curve Pairs According To Type Of Bishop Frame In Lorentz 3-Space

Abstract

The aim of this study is to investigate the associated curves of the normal indicatrix of a non-null curve in Lorentz 3-space. To achieve this goal, firstly, the vectors used in the Frenet elements of the normal indicatrix is utilized to create version of the Bishop frame by taking advantage of the rotations around them. The relationships between the elements of the obtained frames and the associated curves of the normal indicatrix is examined. Additionally, the similarities of these associated curves to the evolute, Mannheim, and Bertrand curve pairs, which are commonly encountered in differential geometry, are studied.