Browsing by Author "Milousheva, Velichka"
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Item Meridian surfaces in E4 with pointwise 1-type Gauss map(Korean Mathematical, 2014-05) Milousheva, Velichka; Arslan, Kadri; Bulca, Betül; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5861-0184; 0000-0002-1440-7050; AAG-8775-2021; AAG-7693-2021; 6603079141; 35226209600In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Further, we give necessary and sufficient conditions for a meridian surface to have pointwise 1-type Gauss map and find all meridian surfaces with pointwise 1-type Gauss map.Item Meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map in Minkowski 4-space(Mathematical Soc Rep China, 2015-08-03) Milousheva, Velichka; Atıf Gayri Ticari Türetilemez 4.0 Uluslararası; Arslan, Kadri; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1440-7050; AAG-8775-2021; 6603079141In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. They are called meridian surfaces of elliptic or hyperbolic type, respectively. We study these surfaces with respect to their Gauss map. We find all meridian surfaces of elliptic or hyperbolic type with harmonic Gauss map and give the complete classification of meridian surfaces of elliptic or hyperbolic type with pointwise 1-type Gauss map.Item Meridian surfaces with constant mean curvature in pseudo-euclidean 4-space with neutral metric(Springer, 2017-02-10) Milousheva, Velichka; Bulca, Betül; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5861-0184; AAG-7693-2021; 35226209600In the present paper we consider a special class of Lorentz surfaces in the four-dimensional pseudo-Euclidean space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with timelike, spacelike, or lightlike axis and call them meridian surfaces. We give the complete classification of minimal and quasi-minimal meridian surfaces. We also classify the meridian surfaces with non-zero constant mean curvature.