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Yayın Classification of minimal Lorentzian surfaces in S-2(4) (1) with Constant Gaussian and normal curvatures(Mathematical Society of The Repulic Of China, 2016-12) Dursun, Uğur; Turgay, Nurettin CenkIn this paper we consider Lorentzian surfaces in the 4-dimensional pseudo Riemannian sphere S-2(4)(1) with index 2 and curvature one. We obtain the complete classification of minimal Lorentzian surfaces S-2(4)(1) whose Gaussian and normal curvatures are constants. We conclude that such surfaces have the Gaussian curvature 1/3 and the absolute value of normal curvature 2/3. We also give some explicit examples.Yayın Rotational Weingarten surfaces in hyperbolic 3-space(Birkhauser, 2020-04-01) Dursun, UğurWe study rotational Weingarten surfaces in the hyperbolic space H3(- 1) with the principal curvatures κ and λ satisfying a certain functional relation κ= F(λ) for a given continuous function F. We determine profile curves of such surfaces parameterized in terms of the principal curvature λ. Then we consider some special cases by taking F(λ) = aλ+ b and F(λ) = aλm for particular values of the constants a, b, and m.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.
