Spherical Images & Characterizations of Time-like Curve According to New Version of The Bishop Frame in 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 time-like curve and call this fame 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 an example of our main results.