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NOTE ON BERTRAND B-PAIRS OF CURVES IN MINKOWSKI 3-SPACE
Ilarslan, Kazim,Ucum, Ali,Aslan, Nihal Kilic,Nesovic, Emilija The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.3
In this paper, we define null Cartan and pseudo null Bertrand curves in Minkowski space ${\mathbb{E}}^3_1$ according to their Bishop frames. We obtain the necessary and sufficient conditions for pseudo null curves to be Bertand B-curves in terms of their Bishop curvatures. We prove that there are no null Cartan curves in Minkowski 3-space which are Bertrand B-curves, by considering the cases when their Bertrand B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo null Bertrand B-curve pairs.
NOTE ON BERTRAND B-PAIRS OF CURVES IN MINKOWSKI 3-SPACE
( Kazim Ilarslan ),( Ali Ucum ),( Nihal Kilic Aslan ),( Emilija Nesovic ) 호남수학회 2018 호남수학학술지 Vol.40 No.3
In this paper, we define null Cartan and pseudo null Bertrand curves in Minkowski space E according to their Bishop frames. We obtain the necessary and sufficient conditions for pseudo null curves to be Bertand B-curves in terms of their Bishop curva-tures. We prove that there are no null Cartan curves in Minkowski 3-space which are Bertrand B-curves, by considering the cases when their Bertrand B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo null Bertrand B-curve pairs.
POSITION VECTORS OF A SPACELIKE W-CURVE IN MINKOWSKI SPACE 𝔼<sub>1</sub><sup>3</sup>
Ilarslan, Kazim,Boyacioglu, Ozgur Korean Mathematical Society 2007 대한수학회보 Vol.44 No.3
In this paper, we study the position vectors of a spacelike W-curve (or a helix), i.e., curve with constant curvatures, with spacelike, timelike and null principal normal in the Minkowski 3-space $\mathbb{E}_1^3$. We give some characterizations for spacelike W - curves whose image lies on the pseudohyperbolical space $\mathbb{H}_0^2$ and Lorentzian sphere $\mathbb{S}_1^2$ by using the positions vectors of the curve.
CURVE COUPLES AND SPACELIKE FRENET PLANES IN MINKOWSKI 3-SPACE
Ucum, Ali,Ilarslan, Kazim,Karakus, Siddika Ozkaldi The Honam Mathematical Society 2014 호남수학학술지 Vol.36 No.3
In this study, we have investigated the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space $\mathbb{E}_1^3$ also is any spacelike Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.
ON TIMELIKE BERTRAND CURVES IN MINKOWSKI 3-SPACE
( Ali Ucum ),( Kazim Ilarslan ) 호남수학회 2016 호남수학학술지 Vol.38 No.3
In this paper, we study the timelike Bertrand curves in Minkowski 3-space. Since the principal normal vector of a timelike curve is spacelike, the Bertrand mate curve of this curve can be a timelike curve, a spacelike curve with spacelike principal normal or a Cartan null curve, respectively. Thus, by considering these three cases, we get the necessary and sufficient conditions for a timelike curve to be a Bertrand curve. Also we give the related examples.
ON TIMELIKE BERTRAND CURVES IN MINKOWSKI 3-SPACE
Ucum, Ali,Ilarslan, Kazim The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.3
In this paper, we study the timelike Bertrand curves in Minkowski 3-space. Since the principal normal vector of a timelike curve is spacelike, the Bertrand mate curve of this curve can be a timelike curve, a spacelike curve with spacelike principal normal or a Cartan null curve, respectively. Thus, by considering these three cases, we get the necessary and sufficient conditions for a timelike curve to be a Bertrand curve. Also we give the related examples.
A NEW APPROACH FOR CHARACTERIZATION OF CURVE COUPLES IN EUCLIDEAN 3-SPACE
Karakus, Siddika Ozkaldi,Ilarslan, Kazim,Yayli, Yusuf The Honam Mathematical Society 2014 호남수학학술지 Vol.36 No.1
In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.
On Pseudo Null Bertrand Curves in Minkowski Space-time
Gok, Ismail,Nurkan, Semra Kaya,Ilarslan, Kazim Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.4
In this paper, we prove that there are no pseudo null Bertrand curve with curvature functions $k_1(s)=1$, $k_2(s){\neq}0$ and $k_3(s)$ other than itself in Minkowski spacetime ${\mathbb{E}}_1^4$ and by using the similar idea of Matsuda and Yorozu [13], we define a new kind of Bertrand curve and called it pseudo null (1,3)-Bertrand curve. Also we give some characterizations and an example of pseudo null (1,3)-Bertrand curves in Minkowski spacetime.