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Günay Öztürk

Publications and source records attributed to Günay Öztürk.

6 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↗
arXiv2016

A characterization of involutes and evolutes of a given curve in $\mathbb{E}^{n}$

The 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 $\mathbb{E}^{n}$. 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 $\mathbb{E}^{n}$. Further, we obtain some results on these type of curves in $\mathbb{E}^{3}$ and $\mathbb{E}^{4}$, respectively.

math.DG↗
arXiv2015

Pseudo-Riemannian Submanifolds with 3-Planar Geodesics

In the present paper we study pseudo-Riemannian submanifolds which have 3-planar geodesic normal sections.We consider W-curves (helices) on pseudo-Riemannian submanifolds. Finally, we give neccessary and sufficient condition for a normal section to be a W-curve on pseudo-Riemannian submanifolds.

math.DG↗