arXiv subjects

Yusuf Yayli

Publications and source records attributed to Yusuf Yayli.

35 records · Page 2Linked to original sources

arXiv2012

On f-Eikonal Helices And f-Eikonal Slant Helices In Riemannian Manifolds

In this paper, we define f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Also, we give the definition of harmonic curvature functions related to f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Moreover, we give characterizations for f-eikonal helix curves and f-eikonal V_{n}-slant helix curves by making use of the harmonic curvature functions.

math.DG↗

arXiv2012

A new approach on helices in Euclidean n-space

In this work, we give some new characterizations for inclined curves and slant helices in n-dimensional Euclidean space E^{n}. Morever, we consider the pre-characterizations about inclined curves and slant helices and reconfigure them.

math.DG↗

arXiv2012

Parallel Transport Frame in 4-dimensional Euclidean Space

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the first time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The condition in terms of κand τ is so complicated but in terms of k_{1} and k_{2} is simple. So, parallel transport frame is important to make easy some complicated characterizations. Moreover, we characterize curves whose position vectors lie in their normal, rectifying and osculating planes in 4-dimensional Euclidean space E^{4}.

math.DG↗

arXiv2012

On weak r-Helix submanifolds

In this paper, we investigate special curves on a weak r-helix submanifold in Euclidean n-space E^{n}. Also, we give the important relations between weak r-helix submanifolds and the special curves such as line of curvature, asymptotic curve and helix line.

math.DG↗

arXiv2012

On Helices and Bertrand Curves in Euclidean 3-Space

In this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show that the curves corresponding to the spherical images of its the tangent indicatrix and binormal indicatrix are both Bertrand curves and circular helices. Similarly, in case of a space curve is a slant helix, we demonstrate that the curve corresponding to the spherical image of its the principal normal indicatrix is both a Bertrand curve and a circular helix.

math.DG↗

arXiv2012

On r-Helix Hypersurfaces

In this paper, we study strong r-helix hypersurfaces and the special curves on these surfaces. Moreover, we investigated the relations between strong r-helix hypersurfaces and the Gauss transformations of these surfaces in Euclidean n-space.

math.DG↗

arXiv2012

On Strong r-Helix Submanifolds and Special Curves

In this paper, we investigate special curves on a strong r-helix submanifold in Euclidean n-space E n. Also, we give the important relations between strong r-helix submanifolds and the special curves such as line of curvature, geodesic and slant helix.

math.DG↗

arXiv2012

Constant Angle Ruled Surfaces in Euclidean Spaces

In this paper, we study the special curves and ruled surfaces on helix hypersurface whose tangent planes make a constant angle with a fixed direction in Euclidean n-space Besides, we observe some special ruled surfaces in and give requirement of being developable of the ruled surface. Also, we investigate the helix surface generated by a plane curve in Euclidean 3-space .

math.DG↗

arXiv2012

The relation between parameter curves and lines of curvature on canal surfaces

A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t). In this paper, we investigate when parameter curves of the canal surface are also lines of curvature. Last of all, for special spine curves we obtain the radius function of canal surfaces.

math.DG↗

arXiv2012

On isophote curve and its characterizations

Isophote comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. Main objective of this paper is to find the axis of an isophote curve via its Darboux frame and afterwards to give some characterizations about isophote and its axis. Particularly, for isophotes lying on a canal surface will be obtained other characterizations again.

math.DG↗

arXiv2012

Lc helices and harmonic curvatures in space forms (hypersurface)

In n-dimensional Euclidean space E^n, harmonic curvatures of a non-degenerate curve defined by Özdamar and Hacisalihoğlu [4]. In this paper, We define a new type of curves called LC helix when the angle between tangent of this curve and LC parallel vector field in space form is constant. Furthermore, several characterizations of these curves by using its harmonic curvatures are obtained. Particularly, in the 3-dimensional spaceform we obtain the results [5].

math.DG↗

arXiv2012

Split Quaternions and Spacelike Constant Slope Surfaces in Minkowski 3-Space

A spacelike surface in the Minkowski 3-space is called a constant slope surface if its position vector makes a constant angle with the normal at each point on the surface. These surfaces completely classified in [J. Math. Anal. Appl. 385 (1) (2012) 208-220]. In this study, we give some relations between split quaternions and spacelike constant slope surfaces in Minkowski 3-space. We show that spacelike constant slope surfaces can be reparametrized by using rotation matrices corresponding to unit timelike quaternions with the spacelike vector parts and homothetic motions. Subsequently we give some examples to illustrate our main results.

math-ph↗

arXiv2012

Characterizations of Special Curves

In this study, the new characterizations of special curves are investigated without using the curvatures of these special curves: general helices, slant helices, Bertrand curves, Mannheim curves. The curvatures are given by the help of the norms of the derivatives of Frenet vectors.

math.DG↗

arXiv2012

On Timelike and Spacelike Developable Ruled Surfaces

In this study, we have obtained the distribution parameter of a ruled surface generated by a straight line in Frenet trihedron moving along a timelike curve and also along another curve with the same parameter. At this time, the Frenet frames of these timelike curves are not the same. We have moved the director vector of the first curve along the second curve. It is shown that the ruled surface is developable if and only if the base timelike curve is helix. In addition, some smilarities and differences are presented with theorems and results.

math.DG↗

arXiv2012

Some Characterizations of Euler Spirals in E_1^{3}

In this study, some characterizations of Euler spirals in E_1^{3} have been presented by using their main property that their curvatures are linear. Moreover, discussing some properties of Bertrand curves and helices, the relationship between these special curves in E_1^{3} have been investigated with different theorems and examples. The approach we used in this paper is useful in understanding the role of Euler spirals in E_1^{3} in differential geometry.

math.DG↗

arXiv2012

Special Space Curves Characterized by det(α^{(3)}, α^{(4)},α^{(5)})=0

In this study, by using the facts that det(α^{(1)}, α^{(2)}, α^{(3)}) = 0 characterizes plane curve, and det(α^{(2)}, α^{(3)}, α^{(4)}) = 0 does a curve of constant slope, we give the special space curves that are characterized by det(α^{(3)}, α^{(4)}, α^{(5)}) = 0, in different approaches. We find that the space curve is Salkowski if and only if det(α^{(3)}, α^{(4)}, α^{(5)}) = 0. The approach we used in this paper is useful in understanding the role of the curves that are characterized by det(α^{(3)}, α^{(4)}, α^{(5)})=0 in differential geometry.

math.DG↗

arXiv2011

On Slant Helices and General Helices in Euclidean n-Space

In this paper, in Euclidean n -space, we investigate the relation between slant helices and spherical helices. Moreover, in E n, we show that a slant helix and the tangent indicatrix of the slant helix have the same axis (or direction). Also, we give the important relations between slant helices, spherical helices in E n and geodesic curves on a helix hypersurface in E n.

math.DG↗