Based on the fundamental theories of null curves in Minkowski 3-space, Darboux mate a curve are defined which can be regarded as kind extension for Bertrand and Mannheim 3-space. The relationships pairs explored their expression forms presented explicitly.

We give a differential geometric interpretation for the classification of biharmonic curves in semi-Euclidean 3-space due to Chen and Ishikawa (1991).

In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set {K, KII , H, HII}, where (K,H) and (KII , HII) are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.

The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.