8 citations · 49 across the 24 of their papers we have counts for
27 papers
Slant helices and Darboux helices in Myller Configuration
Akın Alkan, Mehmet Önder
In this paper, we study slant helix (or -helix) and Darboux helix in Myller configuration . We show that a curve in is a slant helix if and only if it is…
Osculating mate of a Frenet curve in the Euclidean 3-space
Akın Alkan, Mehmet Önder
A new kind of partner curve called osculating mate of a Frenet curve is introduced. Some characterizations for osculating mate are obtained and using the obtained results some spec…
Generalized Normal Ruled Surface of a Curve in the Euclidean 3-space
Onur Kaya, Mehmet Önder
In this study, we define the generalized normal ruled surface of a curve in the Euclidean 3-space . We study the geometry of such surfaces by calculating the Gaussian and mean…
A New Approach to Non-lightlike Curve Pairs
Zehra Ekinci, Mehmet Önder
In this paper, we introduce a new approach to non-lightlike curve pairs by using integral curves in Minkowski 3-space. We consider direction curve and donor curve to study non-ligh…
Construction of curve pairs and their applications
Mehmet Önder
In this study, we introduce a new approach to curve pairs by using integral curves. We consider the direction curve and donor curve to study curve couples such as involute-evolute…
Non-null Slant Ruled Surfaces
Mehmet Önder
In this study, we define some new types of non-null ruled surfaces called slant ruled surfaces in the Minkowski 3-space E_1^3. We introduce some characterizations for a non-null ru…
Construction of a surface pencil with a common special surface curve
Onur Kaya, Mehmet Önder
In this study, we introduce a new type of surface curves called D-type curve. This curve is defined by the property that the unit Darboux vector W0 of a space curve r(s) and unit s…
Mannheim Curves in the three-dimensional Sphere
Tanju Kahraman, Mehmet Onder
Mannheim curves are defined for immersed curves in 3-dimensional sphere S^3 . The definition is given by considering the geodesics of S^3. First, two special geodesics, called prin…
Characterizations of Slant Ruled Surfaces in the Euclidean 3-space
Mehmet Önder, Onur Kaya
In this study, we give the relationships between the conical curvatures of ruled surfaces drawn by the unit vectors of the ruling, central normal and central tangent of a regular r…
Darboux Slant Ruled Surfaces
Mehmet Önder, Onur Kaya
In this study, we introduce Darboux slant ruled surfaces in the Euclidean 3-space which is defined by the property that the Darboux vector of orthonormel frame of ruled surface mak…
Eikonal Slant Helices and Eikonal Darboux Helices In 3-Dimensional Riemannian Manifolds
Mehmet Önder, Evren Ziplar, Onur Kaya
In this study, we give definitions and characterizations of eikonal slant helix curves, eikonal Darboux helices and non-normed eikonal Darboux helices in three dimensional Riemanni…
Dual Smarandache Curves and Smarandache Ruled Surfaces
Tanju Kahraman, Mehmet Önder, H. Hüseyin Uğurlu
In this paper, by considering dual geodesic trihedron (dual Darboux frame) we define dual Smarandache curves lying fully on dual unit sphere S^2 and corresponding to ruled surfaces…
Quaternionic Similar Curves in 4-dimensional Euclidean Space
Mehmet Önder
In this paper, we introduce the quaternionic similar curves in 4-dimensional Euclidean space. We show that the families of quaternionic curves with vanishing curvatures form the fa…
Quaternionic Salkowski Curves and Quaternionic Similar Curves
Mehmet Önder
In this paper, we give the definitions and characterizations of quaternionic Salkowski, quaternionic anti-Salkowski and quaternionic similar curves in the Euclidean spaces E^3 and…
Some Theorems on Timelike Ruled Surfaces
Mehmet Önder
In this study, we investigate the existence theorems for timelike ruled surfaces in Minkowski 3-space. We obtain a general system and give the existence theorems for a timelike rul…
Dual Darboux Frame of a Spacelike Ruled Surface and Darboux Approach to Mannheim Offsets of Spacelike Ruled Surfaces
Mehmet Önder, H. Hüseyin Uğurlu
In this paper, we define dual geodesic trihedron(dual Darboux frame) of a spacelike ruled surface. Then, we study Mannheim offsets of spacelike ruled surfaces in dual Lorentzian sp…
Some Characterizations of Mannheim Partner Curves in Minkowski 3-space
Tanju Kahraman, Mehmet Önder, Mustafa Kazaz +1
In this paper, we give the characterizations of Mannheim Partner Curves in Minkowski 3-space . Firstly, we classify these curves in . Next, we give some relationships characterizin…
Mannheim Offsets of the Timelike Ruled Surfaces with Spacelike Rulings in Dual Lorentzian Space
Mehmet ONder, H. Huseyin Ugurlu
In this paper, we obtain the characterizations of Mannheim offsets of the timelike ruled surface with spacelike rulings in dual Lorentzian space. We give the relations between term…
Spacelike helices in Minkowski 4-Space
Mehmet Önder, Hüseyin Kocyiğit, Mustafa Kazaz
In this paper, we give some characterizations for spacelike helices in Minkowski space-time. We find the differential equations characterizing the spacelike helices and also give t…
Some Results and Characterizations for Mannheim Offsets of the Ruled Surfaces
Mehmet Önder, H. Hüseyin Uğurlu
In this study, we give the dual characterizations of Mannheim offsets of the ruled surface in terms of their integral invariants and the new characterization of the Mannheim offset…
Spacelike B2-Slant Helix in Minkowski 4-Space
Mehmet Önder, Hüseyin Kocayiğit, Mustafa Kazaz
In this paper, we give the characterizations of spacelike B2-slant helix by means of curvatures of the spacelike curve in Minkowski 4-space. Furthermore, we give the integral chara…
Bertrand Partner D-Curves in Minkowski 3-space
Mustafa Kazaz, H. Huseyin Ugurlu, Mehmet Onder +1
In this paper, we consider the idea of Bertrand curves for curves lying on surfaces in Minkowski 3-space. By considering the Darboux frame, we define these curves as Bertrand D-cur…
Bertrand Partner D-Curves in Euclidean 3-space
Mustafa Kazaz, H. Hüseyin Uğurlu, Mehmet Önder +1
In this paper we consider the idea of Bertrand curves for curves lying on surfaces and by considering the Darboux frames of them we define these curves as Bertrand D-curves and giv…
Mannheim Partner D-Curves in Minkowski 3-space
Mustafa Kazaz, H. Hüseyin Uğurlu, Mehmet Önder +1
In this paper, we give the definition, different types and characterizations of Mannheim partner D-curves in Minkowski 3-space. We find the relations between the geodesic curvature…