The Frenet and Darboux instantaneous rotation vectors of curves on time-like surface (Q1275776)

Summary: In this paper, depending on the Darboux instantaneous rotation vector of a solid perpendicular trihedron in the Minkowski 3-space \(\mathbb{R}^3_1=[\mathbb{R}^3,(+,+,-)\)], the Frenet instantaneous rotation vector is obtained for a space-like curve \(c\) with the principal normal \(n\) being a time-like vector. The Darboux instantaneous rotation vector for the Darboux trihedron is found when the curve \(c\) is on a time-like surface. Some theorems and results giving the relations between two frames are stated and proved.