In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space.

In this paper, we investigate special spacelike Smarandache curves of timelike curves according to Sabban frame in Anti de Sitter 3-Space. Moreover, we give the relationship between the base curve and its Smarandache curve associated with theirs Sabban Frames.

In di⁄erential geometry, there are many important consequences and properties of curves studied by some authors. Researchers always introduce some new curves by using the existing studies.

As it is well-known, the geometry of curve in three-dimensions is actually characterized by Frenet vectors. In this paper, we obtain Smarandache curves by using cone frame formulas in null cone Q3 . Also, we give an example related to these curves.

In this paper, we give Darboux approximation for dual Smarandache curves of timelike curve on unit dual Lorentzian sphere.

In this paper, we study the Smarandache curves according to the asymptotic orthonormal frame in Null Cone Q3. By using cone frame formulas, we obtain some characterizations of the Smarandache curves and introduce cone frenet invariants of these curves.

In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and the uses in various fields, we are interested here to study a special kind of curves called Smarandache curves in Lorentz 3-space.