A New Version of Bishop Frame & Application to Spherical Images of Spacelike Curve in E₁³ Minkowski 3-Space

Abstract

In this work, I introduce a new version of Bishop frame using a common vector field as binormal vector field of a regular curve and call this frame as "Type-2 Bishop frame in E₁³". Thereafter, by translating type-2 Bishop frame vectors to O the center of Lorentzian sphere of three-dimensional Minkowski space, I introduce new spherical images and call them as type-2 Bishop spherical images in E₁³. Serret-Frenet apparatus of these new spherical images are obtained in terms of base curves's type-2 Bishop invariants. Additionally, I express some interesting theorems and illustrate one example of our main results.