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İlim Kişi

Publications and source records attributed to İlim Kişi.

4 recordsLinked to original sources
arXiv2019

Some Characterizations of Focal Surfaces of A Tubular Surface in E^3

Here, we focus on focal surfaces of a tubular surface in Euclidean 3-space E^3: Firstly, we give the tubular surfaces with respect to Frenet and Darboux frames. Then, we define focal surfaces of these tubular surfaces. We get some results for these types of surfaces to become flat and we show that there is no minimal focal surface of a tubular surface in E^3. We give some examples for these type surfaces. Further, we show that u-parameter curves cannot be asymptotic curves and we obtain some results about v-parameter curves of the focal surface M^*.

math.DG↗
arXiv2016

A new characterization of canal surfaces with parallel transport frame in Euclidean space $\mathbb{E}^{4}$

In this study, we consider canal surfaces according to parallel transport frame in Euclidean space $\mathbb{E}^{4}$. The curvature properties of these surfaces are investigated with respect to $k_{1}$, $k_{2}$ and $k_{3}$ which are principal curvature functions according to parallel transport frame. We also give an example of canal surfaces in $\mathbb{E}^{4}.$ Further, we point out that if spine curve $γ$ is a straight line, then $M$ is a Weingarten canal surface and also $M$ is a linear Weingarten tube surface. Finally, the visualization of the projections of canal surfaces in $\mathbb{E}^{3}$ are shown.

math.DG↗