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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 On submanifolds of pseudo-hyperbolic space with 1-type pseudo-hyperbolic gauss map(B. I. Verkin Institute for Low Temperature Physics and Engineering, 2016) Dursun, Uğur; Yeğin, RüyaIn this paper, we examine pseudo-Riemannian submanifolds of a pseudo-hyperbolic space ?m-1 s (-1) ? Em s+1 with finite type pseudo-hyperbolic Gauss map. We begin by providing a characterization of pseudo-Riemannian sub- manifolds in ?m-1 s (-1) with 1-type pseudo-hyperbolic Gauss map, and we obtain the classification of maximal surfaces in ?m-1 2 (-1) ? Em 3 with 1-type pseudo-hyperbolic Gauss map. Then we investigate the submanifolds of ?m-1 s (-1) with 1-type pseudo-hyperbolic Gauss map containing nonzero constant component in its spectral decomposition.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.
