Differential Geometry in different spaces

The aim of the thesis is to study a certain class of curves: Magnetic curves, curves of constant-ratio, etc., or one could focus on some properties of curves. In addition, one can study for example factorable surfaces, affine factorable surfaces, factorable surfaces with density. In a study of these surfaces for example, the focus can lie on the curvatures, log-linear density. It is known that many physical processes can be formulated in the form of curves or surfaces so this thesis is interested in studying some special curves and surfaces in the Euclidean and pseudo-Euclidean spaces and then studying their geometric properties. Among these curves are magnetic curves, spacelike curves, lightlike curves and curves of constant-ratio, in addition to studying some of the geometric properties of these curves. Some of the important surfaces that we have studied are surfaces known as Factorable surfaces which are special cases of Monge surfaces.