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Yayın Space-like surfaces in the Minkowski Space E-1(4) with pointwise 1-type Gauss maps(Springer, 2019-06) Dursun, Uğur; Turgay, Nurettin CenkWe first classify space-like surfaces in the Minkowski space E-1(4), de Sitter space S-1(3), and hyperbolic space H-3 with harmonic Gauss maps. Then we characterize and present a classification of the space-like surfaces with pointwise 1-type Gauss maps of the first kind. We also give some explicit examples.Yayın Pseudo-spherical submanifolds with 1-type pseudo-spherical gauss map(Birkhauser Verlag AG, 2016-05-28) Bektaş, Burcu; Canfes, Elif Özkara; Dursun, UğurIn this work, we study pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify Lorentzian surfaces in a 4-dimensional pseudo-sphere (Formula presented.) with index s, (Formula presented.), and having harmonic pseudo-spherical Gauss map. Then we give a characterization theorem for pseudo-Riemannian submanifolds of a pseudo-sphere (Formula presented.) with 1-type pseudo-spherical Gauss map, and we classify spacelike surfaces and Lorentzian surfaces in the de Sitter space (Formula presented.) with 1-type pseudo-spherical Gauss map. Finally, according to the causal character of the mean curvature vector we obtain the classification of submanifolds of a pseudo-sphere having 1-type pseudo-spherical Gauss map with nonzero constant component in its spectral decomposition.Yayın On spacelike rotational surfaces with pointwise 1-type gauss map(Korean Mathematical Soc, 2015-01) Dursun, UğurIn this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-spade E-1(4) with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in E-1(4).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 On submanifolds with 2-Type Pseudo-Hyperbolic Gauss Map in Pseudo-Hyperbolic space(Birkhauser Verlag AG, 2017-02) Şen, Rüya Yeğin; Dursun, UğurIn this paper, we study pseudo-Riemannian submanifolds of a pseudo-hyperbolic space Hsm-1(-1)?Es+1m with 2-type pseudo-hyperbolic Gauss map. We give a characterization of proper pseudo-Riemannian hypersurfaces in Hsn+1(-1)?Es+1n+2 with non-zero constant mean curvature and 2-type pseudo-hyperbolic Gauss map. For n= 2 , we prove classification theorems. In addition, we show that the hyperbolic Veronese surface is the only maximal surface fully lying in H24(-1)?H2m-1(-1) with 2-type pseudo-hyperbolic Gauss map. Moreover, we prove that a flat totally umbilical pseudo-Riemannian hypersurface Mtn of the pseudo-hyperbolic space Htn+1(-1)?Et+1n+2 has biharmonic pseudo-hyperbolic Gauss map.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 Classification of surfaces in a pseudo-sphere with 2-type pseudo-spherical Gauss map(Wiley-V C H Verlag GMBH, 2017-11) Bektaş, Burcu; Canfes, Elif Özkara; Dursun, UğurIn this article, we study submanifolds in a pseudo-sphere with 2-type pseudo-spherical Gauss map. We give a characterization theorem for Lorentzian surfaces in the pseudosphere S-2(4) subset of E-2(5) with zero mean curvature vector in S-2(4) and 2-type pseudo-spherical Gauss map. We also prove that non-totally umbilical proper pseudo-Riemannian hypersurfaces in a pseudo-sphere S-s(n+1) subset of E-s(n+2) with non-zero constant mean curvature has 2-type pseudo-spherical Gauss map if and only if it has constant scalar curvature. Then, for n = 2 we obtain the classification of surfaces in S-1(3) subset of E-1(4) with 2-type pseudo-spherical Gauss map. Finally, we give an example of surface with null 2-type pseudo-spherical Gauss map which does not appear in Riemannian case, andwe give a characterization theorem for Lorentzian surfaces in S-1(3) subset of E-1(4) with null 2-type pseudospherical Gauss map.Yayın Constant angle surfaces in the Lorentzian warped product manifold – I × fE²(Birkhauser, 2021-06) Dursun, Uğur; Turgay, Nurettin CenkIn this work, we study constant angle space-like and time-like surfaces in the 3-dimensional Lorentzian warped product manifold - I× fE² with the metric g~ = - d t²+ f²(t) (d x²+ d y²) , where I is an open interval, f is a strictly positive function on I, and E² is the Euclidean plane. We obtain a classification of all constant angle space-like and time-like surfaces in - I× fE². In this classification, we determine space-like and time-like surfaces with zero mean curvature, rotational surfaces, and surfaces with constant Gaussian curvature. Also, we obtain some results on constant angle space-like and time-like surfaces of the de Sitter space S13(1).Yayın Hyperbolic submanifolds with finite type hyperbolic Gauss map(World Scientific Publishing Co. Pte Ltd, 2015-02) Dursun, Uğur; Yeğin, RüyaWe study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface M-n with nonzero constant mean curvature in a hyperbolic space Hn+1 subset of E-1(n+2) has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space H-3 subset of E-1(4) having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in Hn+1 subset of E-1(n+2) has biharmonic hyperbolic Gauss map.Yayın Spacelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski Space E-1(4) with pointwise 1-Type Gauss map(Springer, 2014-06) Dursun, Uğur; Bektaş, BurcuIn this paper, we consider a class of spacelike rotational surfaces in Minkowski space E-1(4) with 2-dimensional axis. There are three types of rotational surfaces with 2-dimensional axis, called rotational surfaces of elliptic, hyperbolic or parabolic type. We obtain all flat spacelike rotational surfaces of elliptic and hyperbolic types with pointwise 1-type Gauss map. We also determine flat spacelike rotational surface of parabolic type with pointwise 1-type Gauss map of the first kind. Then, we conclude that there exists no flat spacelike rotational surface of parabolic type in E-1(4) with pointwise 1-type Gauss map of the second kind.
