This work extends some classical results of Bertrand curves to timelike ruled and developable surfaces using the E. Study map. provides support define two which are offset in sense Bertrand. It is proved that every surface has a if only an equation should be satisfied among their dual invariants. In addition, new theorems concerning developability offsets gained.

In this article, spatial quaternionic Bertrand curve pairs in the 3-dimensional Euclidean space are examined. Algebraic properties of quaternions, basic definitions and theorems given. Later, some characterizations obtained space.