Translation framed surfaces generated by non-null framed curves in Minkowski 3-space

Abstract

In this paper, first we obtain the conditions for the existence and uniqueness of non-null framed curves as well as non-null framed surfaces in Minkowski $3$-space. Further, we study the timelike and spacelike translation framed surfaces generated by non-null framed curves and obtain the basic invariants of such surfaces in $\E^3_1$. We also find the curvatures of timelike and spacelike translation framed surfaces generated by non-null framed curves. Finally, we classify the translation framed surfaces generated by non-null framed curves lying in mutually perpendicular coordinate planes of $\E^3_1$ with $\K_K \equiv 0$ and $\K_H \equiv 0$.