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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).
