ASSOCIATED CURVES OF THE SPACELIKE CURVE VIA THE BISHOP FRAME OF TYPE-2 IN E₁³

Abstract

The objective of the study in this paper is to define M₁,M₂-direction curves and M₁,M₂-donor curves of the spacelike curve γ via the Bishop frame of type-2 in E₁³. We obtained the necessary and sufficient conditions when the associated curves to be slant helices and general helices via the Bishop frame of type-2 in E₁³. After defining the spherical indicatrices of the associated curves, we obtain some relations between associated curves and their spherical indicatrices in terms of the frames used in the present work.

Keywords

• minkowski 3-space
• bishop frame of type-2
• m₁m₂-direction curves
• m₁m₂-donor curves
• slant helices