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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.
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.
Curve Couples and Spacelike Frenet Planes in Minkowski 3-Space
( Ali Ucum ),( Kazim Ilarsilan ),( Siddika Ozkaldi Karakus ) 호남수학회 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 E13 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.
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.