Introducing Weingarten cyclic surfaces in R3 Hamdoon, Fathi M.; Abd-Rabo, M.A.
Journal of the Egyptian Mathematical Society,
January 2017, 2017-01-00, Volume:
25, Issue:
1
Journal Article
Peer reviewed
Open access
In this paper, Cyclic surfaces are introduced using the foliation of circles of curvature of a space curve. The conditions on a space curve such that these cyclic surfaces are of type Weingarten ...surfaces or HK-quadric surfaces are obtained. Finally, some examples are given and plotted.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space $\mathbf{E}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant ...Gaussian curvature $K$ if and only if the surface is flat, i.e. $K=0$.
(2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone. KCI Citation Count: 1
In this paper, we present a differential geometric local study of two-parameter spatial motions: we look for points, which (up to the second order) instantaneously move on one-dimensional point ...paths, further we locally characterise these motions, which move ∞
1 points in these way.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator. We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, ...minimal, II-minimal and Weingarten surface. Moreover, the parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica. KCI Citation Count: 1
.
In this paper we present a local study of a cyclic surface in E
5
generated by equiform motions of circles. We describe partially such surfaces with some assumption on its curvature. In general, we ...shall consider the situation that the scalar curvature is locally constant.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this article, we study skew ruled surfaces by using the geodesic Frenet trihedron of its generator. We obtained some conditions on this surface to ensure that this ruled surface is flat, II-flat, ...minimal, II-minimal and Weingarten surface. Moreover, the parametric equations of asymptotic and geodesic lines on this ruled surface are determined and illustrated through example using the program of mathematica.
In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant ...Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.
In this paper we consider the equiform motion of a helix in Euclidean space \(\mathbf{E}^7\). We study and analyze the corresponding kinematic three dimensional surface under the hypothesis that its ...scalar curvature \(\mathbf{K}\) is constant. Under this assumption, we prove that if the scalar curvature \(\mathbf{K}\) is constant, then \(\mathbf{K}\) must equal zero.
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