The Frenet and Darboux instantaneous rotation vectors of curves on time-like surface

Abstract

In this paper, depending on the Darboux instantaneous rotation vector of a solid perpendicular trihedron in the Minkowski 3-space $R_1^3=[R^3, (+,+,-)]$ the Frenet instantaneous rotation vector was stated for a space-Eke curve (c) with the principal normal n being a time-like vector. The Darboux instantaneous rotation vector for the Darboux trihedron was found when the curve (c) is on a time-Eke surface. Some theorems and results giving the relations between two frames were stated and proved.