Person: BULCA SOKUR, BETÜL
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BULCA SOKUR
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BETÜL
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Publication Rotational surfaces with rotations in x3x4-plane(Tsing Hua Univ, Dept Mathematics, 2021-01-01) Arslan, Kadri; Bulca, Betül; ARSLAN, KADRİ; BULCA SOKUR, BETÜL; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0001-5861-0184; EJT-1458-2022; AAG-7693-2021In the present study we consider generalized rotational surfaces in Euclidean 4-space E-4. Further, we obtain some curvature properties of these surfaces. We also introduce some kind of generalized rotational surfaces in E-4 with the choice of meridian curve. Finally, we give some examples.Publication General rotational ξ-surfaces in euclidean spaces(Tubitak Scientific & Technological Research Council Turkey, 2021-01-01) Arslan, Kadri; ARSLAN, KADRİ; Aydın, Yılmaz; Bulca, Betul; BULCA SOKUR, BETÜL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5861-0184The general rotational surfaces in the Euclidean 4-space R-4 was first studied by Moore (1919). The Vranceanu surfaces are the special examples of these kind of surfaces. Self-shrinker flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, xi-surfaces are the generalization of self-shrinker surfaces. In the present article we consider xi-surfaces in Euclidean spaces. We obtained some results related with rotational surfaces in Euclidean xi- space R-4 to become self-shrinkers. Furthermore, we classify the general rotational xi-surfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational xi-surfaces in R-4.Publication A characterization of involutes and evolutes of a given curve in En(Kyungpook Natl Univ, Dept Mathematics, 2018-03-01) Öztürk, Günay; Arslan, Kadri; ARSLAN, KADRİ; Bulca, Betül; BULCA SOKUR, BETÜL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-1440-7050; 0000-0001-5861-0184; AAG-8775-2021; AAG-7693-2021The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space E-n. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space E-n. Further, we obtain some results on these type of curves in E-3 and E-4, respectively.Publication A geometric modeling of tracheal elements of the chard ( beta vulgaris ) leaf(Univ Federal Vicosa, 2019-01-01) Özdemir, Canan; Özdemir, Ali; Bozdağ, Bahattin; Bulca, Betül; BULCA SOKUR, BETÜL; Arslan, Kamil; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi; 0000-0002-1440-7050; 0000-0001-5861-0184; 0000-0002-4466-3901; AAG-7693-2021; N-6684-2019In this study, we give a geometric description of the tracheal elements of the chard (Beta vulgaris var. cicla L.). which is a widespread cultivated plant in Turkey. It is used as an edible plant and its leaves are used as antidiabetic in traditional medicine plant. We have shown that the tracheal elements, which are taxonomic value of the plant, can be considered as a surface of revolution or a tubular shape along a special curve.Publication On constant-ratio surfaces of rotation in euclidean 4-space(World Scientific Publ Co Pte Ltd, 2023-09-27) Arslan, Kadri; Bulca, Betül; Demirbaş, Eray; ARSLAN, KADRİ; BULCA SOKUR, BETÜL; Demirbaş, Eray; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5861-0184; EJT-1458-2022; AAG-7693-2021; ESA-0181-2022The general rotational surfaces of E-4 were first studied by Moore. The Vranceanu surfaces are special examples of this kind of surfaces. These constant-ratio surfaces are surfaces for which the ratio of the norms of the tangent and normal components of the position vector fields is constant. However, spherical surfaces and conical surfaces are also trivial examples of constant-ratio surfaces. Thus, if the norms of the tangent or normal components of the position vector fields are constant, then the given surface is called T-constant or N-constant, respectively. In this paper, we considered three types of rotational surfaces lying in 4-dimensional Euclidean space E-4. We have obtained the necessary and sufficient conditions for these surfaces to satisfy the T-constant, N-constant or constantratio conditions. With the help of these results, we characterized the meridian curves of the surfaces. Further, we also give some examples to support the results obtained.Publication Semi-parallel meridian surfaces in E⁴(Int Electronic Journal Geometry, 2015-10-01) Bulca, Betül; Arslan, Kadri; BULCA SOKUR, BETÜL; ARSLAN, KADRİ; Ulıdağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0001-5861-0184; 0000-0002-1440-7050; AAG-7693-2021; AAG-8775-2021In 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 classify semi-parallel meridian surfaces in 4-dimensional Euclidean space E-4.Publication On generalized spherical surfaces in euclidean spaces(Honam Mathematical Soc, 2017-09-01) Bayram, Bengü; Arslan, Kadri; ARSLAN, KADRİ; Bulca, Betül; BULCA SOKUR, BETÜL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-1440-7050; 0000-0001-5861-0184; AAG-7693-2021In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1) space En+1. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces E-3 and E-4 respectively. We have shown that the generalized spherical surfaces of first kind in E-4 are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in I. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.Publication Semiparallel tensor product surfaces in e 4(Int Electronic Journal Geometry, 2014-04-01) Bulca, Betül; BULCA SOKUR, BETÜL; Arslan, Kadri; ARSLAN, KADRİ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-5861-0184; 0000-0002-1440-7050; AAG-7693-2021; AAG-8775-2021B.Y. Chen initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold. Inspired by Chen's definition, F. Decruyenaere, F. Dillen, L. Verstraelen and L. Vrancken studied the tensor product of two immersions, in general, different manifolds; under certain conditions, this realizes an immersion of the product manifold. Further, tensor product surfaces of Euclidean plane curves were investigated by I.Mihai and B. Rouxel. In the present study we consider the tensor product surfaces in 4-dimensional Euclidean space E-4. We have shown that tensor product surfaces in E(n)satisfying the semiparallelity condition (R) over bar (X, Y). h = 0 are totally umbilical surfaces.Publication General rotational surfaces satisfying ΔxT = φxT(Springer Basel Ag, 2022-02-01) Demirbaş, Eray; Arslan, Kadri; ARSLAN, KADRİ; Bulca, Betül; BULCA SOKUR, BETÜL; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/ Matematik Anabilim Dalı.; 0000-0001-5861-0184In the present study we consider rotational surfaces in Euclidean 4-space whose canonical vector field x(T) satisfy the equality Delta x(T) = phi x(T). Further, we obtain some results related to three types of general rotational surfaces in E-4 satisfying this equality. We also give some examples related with these type of surfaces.