Yazar "Yoon, Dae Won" seçeneğine göre listele

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    2-Ruled hypersurfaces in Euclidean 4-space
    (Elsevier, 2021) Altin, Mustafa; Kazan, Ahmet; Yoon, Dae Won
    In this paper, firstly we obtain the Gauss map (unit normal vector field) of a 2-ruled hypersurface in Euclidean 4-space with the aid of its general parametric equation. After, we obtain Gaussian and mean curvatures of the 2-ruled hypersurface and give some characterizations about its minimality. Finally, we deal with the first and second Laplace-Beltrami operators of 2-ruled hypersurfaces in E-4 and give some results about them. (C) 2021 Elsevier B.V. All rights reserved.
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    CANAL HYPERSURFACES GENERATED BY NON-NULL CURVES IN LORENTZ-MINKOWSKI 4-SPACE
    (Korean Mathematical Soc, 2023) Altin, Mustafa; Kazan, Ahmet; Yoon, Dae Won
    In the present paper, firstly we obtain the general expression of the canal hypersurfaces that are formed as the envelope of a family of pseudo hyperspheres, pseudo hyperbolic hyperspheres and null hypercones whose centers lie on a non-null curve with non-null Frenet vector fields in E14 and give their some geometric invariants such as unit normal vector fields, Gaussian curvatures, mean curvatures and principal curvatures. Also, we give some results about their flatness and minimality conditions and Weingarten canal hypersurfaces. Also, we obtain these characterizations for tubular hypersurfaces in E-1(4) by taking constant radius function and finally, we construct some examples and visualize them with the aid of Mathematica.
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    Generalized rotation surfaces in E4 with density
    (Elsevier, 2023) Kazan, Ahmet; Altin, Mustafa; Yoon, Dae Won
    In the present paper, we obtain the weighted mean and weighted Gaussian curvatures of a generalized rotation surface in E4 with density e lambda 1x2+lambda 2y2+lambda 3z2+lambda 4t2, where lambda i, i is an element of {1, 2, 3, 4}, are not all zero and we give some results about weighted minimal and weighted flat generalized rotation surface in E4 with density e lambda(x2+y2)+mu(z2+t2), where lambda and mu are not all zero. Also, we obtain the weighted mean and weighted Gaussian curvatures of Klein bottle, Banchoff surface, Vranceanu rotation surface, and Clifford torus, which are examples of generalized rotation surfaces, in E4 with density e lambda(x2+y2)+mu(z2+t2) and give some results for their minimality and flatness.(c) 2023 Elsevier B.V. All rights reserved.
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    Geometric characterizations of canal hypersurfaces in Euclidean spaces
    (Univ Nis, Fac Sci Math, 2023) Kazan, Ahmet; Altin, Mustafa; Yoon, Dae Won
    In the present paper, firstly we obtain the general expression of canal hypersurfaces in Euclidean n-space and deal with canal hypersurfaces in Euclidean 4-space E4. We compute Gauss map, Gaussian curvature and mean curvature of canal hypersurfaces in E4 and obtain an important relation between the mean and Gaussian curvatures as 3H rho = K rho 3 - 2. We prove that, the flat canal hypersurfaces in Euclidean 4-space are only circular hypercylinders or circular hypercones and minimal canal hypersurfaces are only generalized catenoids. Also, we state the expression of tubular hypersurfaces in Euclidean spaces and give some results about Weingarten tubular hypersurfaces in E4.