Abstract:In the present study we consider generalized rotation surfaces imbedded in an Euclidean space of four dimensions. We also give some special examples of these surfaces in E 4 . Further, the curvature properties of these surfaces are investigated. We give necessary and sufficient conditions for generalized rotation surfaces to become pseudo-umbilical. We also show that every general rotation surface is Chen surface in E 4 . Finally we give some examples of generalized rotation surfaces in E 4 .Mathematics Subjec… Show more
In this paper, we study the self-similar surfaces in 4-dimensional Euclidean space E 4. We give an if and only if condition for a generalized rotational surfaces in E 4 to be self-similar. In addition we examine self-similarity of some special surfaces in E 4. Furthermore we investigate the self-similar condition of Tensor Product surfaces and Meridian surfaces in E 4 .
In this paper, we study the self-similar surfaces in 4-dimensional Euclidean space E 4. We give an if and only if condition for a generalized rotational surfaces in E 4 to be self-similar. In addition we examine self-similarity of some special surfaces in E 4. Furthermore we investigate the self-similar condition of Tensor Product surfaces and Meridian surfaces in E 4 .
“…The surface given with the parametrization (1.1) is called pencil surface in E 4 . If γ(s) is a W-curve then M becomes a generalized rotation surface defined by Milousheva in [11] and see also [1,5].…”
In this paper, we study the problem of constructing a family of surfaces (surface pencils) from a given curve in 4-dimensional Euclidean space E 4 . We have shown that the generalized rotation surfaces in E 4 are the special type of surface pencils. Further, the curvature properties of these surfaces are investigated. Finally, we give some examples of flat surface pencils in E 4 .
“…When we focus on the rotational characters in the literature, we meet Arslan et al [1,2], Arvanitoyeorgos et al [3], Chen [4,5], Dursun and Turgay [6], Kim and Turgay [7], Takahashi [8], and many others.…”
Section: Introductionmentioning
confidence: 99%
“…They classified completely the minimal rotational surfaces and those consisting of parabolic points. Arslan et al [2] studied generalized rotation surfaces in E 4 . Moreover, Dursun and Turgay [6] studied minimal and pseudo-umbilical rotational surfaces in E 4 .…”
We study and examine the rotational hypersurface and its Gauss map in Euclidean four-space E 4 . We calculate the Gauss map, the mean curvature and the Gaussian curvature of the rotational hypersurface and obtain some results. Then, we introduce the third Laplace–Beltrami operator. Moreover, we calculate the third Laplace–Beltrami operator of the rotational hypersurface in E 4 . We also draw some figures of the rotational hypersurface.
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