الفهرس 
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Abstract
The subject of this thesis is related to a branch of mathematics which is differential geometry. We introduce some forms for Frenet frame equations for some curves in Minkowski space. The effect of some types of geometric transformations as folding, retraction, deformation retract and deformation on curves, surfaces, parallel surfaces, ruled surfaces and hyperbolic surface has been presented. The thesis consists of five chapters: In chapter one: An introduction and presents a brief survey of some fundamental concepts, the main important definitions and notations. In chapter two: A form for Frenet equations of null curves in Minkowski 3-space has been presented. New types of foldings of null curves in and their Frenet equations are obtained. New types of some geometrical transformations of hyperbola in are introduced. In chapter three: A form for Frenet equations of pseudo null space-like curves in Minkowski 3- space has been presented. New types of retractions of curves are obtained. New types of retractions and foldings of helix and their Frenet equations in are achieved In chapter four: The position vector equation of Frenet curves with constant curvatures in Minkowski 4 - space has been presented. New types for retractions and deformation retracts of Frenet curves in are deduced. In chapter five: New types of foldings and retractions on ruled surfaces and parallel ruled surfaces as directrix retraction and ruling retraction in Minkowski 3- space have been presented. Also, the geodesic retractions of the hyperbolic surfaces and are presented.