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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 On pseudo-umbilical rotational surfaces with pointwise 1-type gauss map in E-2(4)(Istanbul Technical Univ, 2017-01-01) Bektaş, Burcu; Canfes, Elif Özkara; Dursun, UğurIn this work, we study two families of rotational surfaces in the pseudo Euclidean space 1E4 with profile curves lying in 2 dimensional planes. First, we obtain a classification of pseudo umbilical spacelike surfaces and timelike surfaces in these families. Then, we show that in this classification there exists no a pseudo umbilical rotational surface in 1E4 with pointwise 1 type Gauss map of second kind. Finally, we determine such pseudo umbilical rotational surfaces in 1E4 having pointwise 1 type Gauss map of first kind.Yayın Slant curves in the Lorentzian warped product manifold - I× fE²(Birkhauser, 2022-03-15) Dursun, UğurIn this work, we study slant curves in the 3-dimensional Lorentzian warped product - I× fE², where E² is a 2-dimensional Euclidean plane, I? R is an open interval equipped with the metric dt², and f is a positive smooth function on I. First we give a characterization of slant curves, and then we obtain a classification of all slant curves in - I× fE². We also compute their curvature and torsion, and we obtaine some results on slant curves and helices in the de Sitter space S13(1) and in the Minkowski space E13. Moreover we determined some biharmonic slant curves in S13(1).
