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.
1], we define the tangent surface M generated by [gamma] as the surface parameterized by
Then the tangent surface generated by [gamma] is a plane, which is a constant angle surface.
A picture of the curve [gamma] and the corresponding tangent surface appears in Figure 2.
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.
In Section 4 we deal with tangent surfaces showing in Theorem 4.
For tangent surfaces x, the unit normal vector field [zeta] to M is [zeta] = ([x.