In differential geometry (CADDEO; MONTALDO, 2001), (DIMITRIC, 1992), (LOUBEAU; ONICIUC, 2007), (O'NEILL, 1983) that under the assumption of sufficient differentiability, a developable surface is either a plane, conical surface, cylindrical surface or tangent surface
of a curve or a composition of these types.
Given a regular curve [gamma] : I [right arrow] [E.sup.3.sub.1], we define the tangent surface M generated by [gamma] as the surface parameterized by
Conversely, let [gamma] = [gamma](s) be a helix and let x = x(s, t) be the corresponding tangent surface. We know that [tau]/[kappa] is a constant function.
Figure 3 shows the curve [gamma] and the generated tangent surface.
Let M be a tangent surface generated by a curve [gamma] such that M is timelike.
To separate a tangent surface according to Sabban frame from that of Frenet- Serret frame, in the rest of the paper, we shall use notation for this surface as S--tangent surface.
The purpose of this section is to study S tangent surfaces of timelike biharmonic S-curve in the Lorentzian Heisenberg group [Heis.sup.3].