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Yayın Graph surfaces invariant by parabolic screw motions with constant curvature in H²×R(DergiPark, 2023-04-30) Dursun, UğurIn this work we study vertical graph surfaces invariant by parabolic screw motions with pitch ? > 0 and constant Gaussian curvature or constant extrinsic curvature in the product space H² × R. In particular, we determine flat and extrinsically flat graph surfaces in H² × R. We also obtain complete and non-complete vertical graph surfaces in H² × R with negative constant Gaussian curvature and zero extrinsic curvature.Yayın Constant angle surfaces in the Lorentzian warped product manifold I ×f E²1(Tübitak, 2022-09-14) Dursun, UğurLet I ×f E²1 be a 3-dimensional Lorentzian warped product manifold with the metric g˜ = dt² + f² (t)(dx² ? dy² ), where I is an open interval, f is a strictly positive smooth function on I, and E²1 is the Minkowski 2-plane. In this work, we give a classification of all space-like and time-like constant angle surfaces in I ×f E²1 with nonnull principal direction when the surface is time-like. In this classification, we obtain space-like and time-like surfaces with zero mean curvature, rotational surfaces, and surfaces with constant Gaussian curvature. Also, we have some results on constant angle surfaces of the anti-de Sitter space H³1(?1).Yayın Surfaces with constant Gaussian and mean curvatures N the anti-de Sitter space H31(Honam Mathematical Soc, 2024-06) Dursun, UğurIn this work, we study time-like and space-like surfaces invariant by a group of translation isometries of the half-space model H31 of the anti-de Sitter space H31. We determine all such surfaces with constant mean curvature and constant Gaussian curvature. We also obtain umbilical surfaces of H31.Yayın The Killing magnetic curves in the anti-de Sitter space H31(TUBITAK, 2026-03-10) Dursun, UğurIn this paper, we study space-like, time-like and light-like Killing magnetic curves derived from Killing magnetic vector fields of the anti-de Sitter space H31 by using the half-space model H31 of H31 . We find the first integrals of the system of nonlinear differential equations that describe the Killing magnetic curves corresponding to some Killing vector fields of H31 , and then we give some particular solutions to obtain space-like, time-like and light-like magnetic curves of H31 . Also, we calculate the curvature and torsion of some space-like and time-like Killing magnetic curves, and the torsion of light-like Killing magnetic curves of H31.
