Geometric properties of special surfaces

In this Ph.D thesis, the canal ve tube surfaces are studied in Euclid, Galilean and pseudo 4-dimensional pseudo-Euclid spaces with 2 index and in addition the rotated surfaces are studied in Galilean 3-space. Firstly, a similar group of rotational matrices are done on the isometries defined in pseudo-Riemannian manifold. Thus, different types of rotational matrices are obtained in Galilean space. To create these matrices, Killing vector fields are required. Therefore, Killing vector fields corresponding to isotropic vectors are attained in Galilean space. On rotated surface obtained by using this vector field, the consepts of \Phi(H,K)-Weingarten surface, flat, harmonic and HK-quadric surface are examined. Also, some characterizations related to canal surfaces obtained using these curves are given and their physical interpretation is made. Finally, normal curves are expressed. Some characterization on canal surfaces obtained using normal curves are given. Moreover, on surface that is obtained, by using mean curvature H and Gauss curvature K, \Phi(H,K)-Weingarten surface, $HK$-quadric surface, flat and minimal surfaces are examined.