A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve.

In this paper, we introduce special equiform Smarandache curves reference to the equiform Frenet frame of a curve on a spacelike surface M in Minkowski 3-space E31.

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 introduce some special Smarandache curves according to Bishop frame in Euclidean 3-space E3.

In Smarandache geometry, a regular non-null curve in Minkowski 3-space, whose position vector is collected by the Frenet frame vectors of other regular non-null curve, is said to be Smarandache curve.

In this paper, we introduce the equiform-Bishop frame of a spacelike curve r lying fully on S21 in Minkowski 3-space R31. By using this frame, we investigate the equiform-Bishop Frenet invariants of special spacelike equiform-Bishop Smarandache curves of a spacelike base curve in R31 . Furthermore, we study the geometric properties of these curves when the spacelike base curve r is specially contained in a plane. Finally, we givea computational example to illustrate these curves.

In this paper, we define Smarandache curves of null quaternionic curves in the semi-Euclidean space 31E and obtaine that curvatures of null quaternionic curves have some relations for Smarandache curves.

A third order vectorial differential equation of position vector of Smarandache breadth curves has been obtained 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 this paper, we investigate Smarandache curves according to type-2 Bishop frame in Euclidean 3- space and we give some differential geometric properties of Smarandache curves.