Murat Kemal Karacan

Bu çalışmada, üç boyutlu De Sitter uzayında 𝐾 − flat ve minimal dönel yüzeyleri ve yüzeyin pozisyon vektörünü kullanacarak laplace operatörünün Δ𝑋 = 0, Δ𝑋 = 𝜆𝑋 ve Δ𝑋 = 𝐴𝑋 eşitliğini sağlayan konformal ve non konformal yüzeyleri araştırdık.

In this section, we have defined some of the special affine surfaces(Affine spheres, Affine ruled surfaces) and their dual surfaces given by the monge patch in Simply Isotropic 3-space. We also have given the Gaussian and the mean curvatures.

In this paper, we study translation surfaces in three dimensional affine space. We characterize the finite type non-degenerate translation surfaces with respect to the first affine and the second affine fundamental forms.

In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices.

In this paper, we give the classification of the LCN-translation surfaces with zero mean curvature and zero Gaussian curvature in 3-dimensional Affine space.

In this paper, we study helices and the Bertrand curves. We obtain some of the classification results of these curves with respect to the modified orthogonal frame in Euclidean 3-spaces.

In this paper, we classify two types ruled surfaces in the three dimensional simply isotropic space I¹ ₃ under the condition ∆x_i= λ_ix_i where ∆ is the Laplace operator with respect to the first fundamental form and λ is a real number. We also give explicit forms of these surfaces.