Bahaddin Bükcü - Academia.edu (original) (raw)

Papers by Bahaddin Bükcü

Research paper thumbnail of Bishop frame of the spacelike curve with a spacelike principal normal in Minkowski 3-space

Bu çalışmada, Bishop [1] tarafından yapılan çalışmayı, spacelike asli normalli spacelike eğriler ... more Bu çalışmada, Bishop [1] tarafından yapılan çalışmayı, spacelike asli normalli spacelike eğriler için Minkowski 3-uzayına genelleştirdik. İlaveten, spacelike eğriler için Bishop Darboux vektörü (matrisi) bulundu. Ayrıca, spacelike eğrinin T teğet vektörünün türevi kullanılarak, (K,\tau) ve (k_1,k_2) eğrilik fonksiyonları arasındaki ilişkiler bulundu.In this study, we generalize for a spacelike curve with a spacelike principal normal which was studied by Bishop [1] to Minkowski 3-Space. In addition, the Bishop Darboux vector (matrix) for spacelike curve is found. Furthermore, using the derivative of the tangent vector T of the spacelike curve, the relations between the curvature funtions K,\tau and k_1,k_2 is found

Research paper thumbnail of The Relation Between Base Curve of the Ruled Surface and It's Adjoint Curve

Research paper thumbnail of Sdü Fen Edebi̇yat Fakültesi̇ Fen Dergi̇si̇ (E-Dergi̇). 2008, 3(1), 80-90 Bishop Frame of the Timelike Curve in Minkowski 3-SPACE

In this study, we study the result which are obtained by BISHOP (1975) for a timelike curve in Mi... more In this study, we study the result which are obtained by BISHOP (1975) for a timelike curve in Minkowski 3-Space.In addition , the Darboux vector(matrix) for the timelike curve is found. Furthermore, using the derivative of the tangent vector T of the timelike curve, the relations between the curvature funtions τ κ , and 2 1 , k k are found.

Research paper thumbnail of New Characterizations For Bertrand Curves In Minkowski 3-Space

Bertrand curves have been investigated in Lorentzian and Minkowski spaces and some characterizati... more Bertrand curves have been investigated in Lorentzian and Minkowski spaces and some characterizations have been given in [1,2,6]. In this paper, we have investigated the relations between Frenet vector fields and curvatures and torsions of Bertrand curves at the corresponding points in Minkowski 3-space.

Research paper thumbnail of Minkowski 3-UZAYINDA Ti̇meli̇ke Eğri̇ni̇n Bi̇shop Çatisi

Biz bu calismada, BISHOP (1975) tarafindan elde edilen sonucu, Minkowski 3- uzayinda timelike egr... more Biz bu calismada, BISHOP (1975) tarafindan elde edilen sonucu, Minkowski 3- uzayinda timelike egriler icin calistik. Ilaveten, timelike egriler icin Darboux vectoru(matrisi) bulundu. Ayrica, timelike egrinin T teget vektorunun turevi kullanilarak κ,τ ve 1 2 k , k egrilik fonksiyonlari arasindaki iliskiler bulundu.

Research paper thumbnail of Ökli̇d Uzayinda Genel Cayley Dönüşümü Ve Dönme Matri̇sleri̇

Bu calismada, bir S anti-simetrik matrisi icin Cayley donusumu tanimlandi [1]. Anti-simetrik matr... more Bu calismada, bir S anti-simetrik matrisi icin Cayley donusumu tanimlandi [1]. Anti-simetrik matrislerle vektorler arasindaki bazi bagintilar verildi. Daha sonra, bir F donusumu tanimlandi. F donusu icin f (S) = I + S secildiginde, F(S) nin Cayley donusumune karsilik geldigi gosterildi. 2 f (S) = I − aS + bS secilme durumu da, Genel Cayley donusumu olarak adlandirildi. F(S) = A matrisinin pozitif ortogonal oldugu ve S ↔ s eksenini degismez biraktigi gosterildi. Boylece, F donusumunun s ekseni etrafinda belli bir donme yaptigi gosterildi. Ayrica 4 E , n E donme matrisleri belli sartlar altinda elde edildi ve iki Cayley matrisinin carpimina karsilik gelen eksen de bulundu.

Research paper thumbnail of E ’de TIME-LIKE BİR EĞRİ İÇİN ÖZEL BİR FRENET HAREKETİNİN DARBOUX VEKTÖRLERİ ÜZERİNE

Bir parametreli ozel Frenet hareketi, Bottema tarafindan 3-boyutlu Oklid uzayi E3 de verilmistir ... more Bir parametreli ozel Frenet hareketi, Bottema tarafindan 3-boyutlu Oklid uzayi E3 de verilmistir [1]. Bu calismada, E3 deki [1] Frenet hareketinin, 3 E1 , 3-boyutlu Minkowski uzayina bir genellestirilmesi veriliyor. Ilk olarak, E3 deki bu hareket, time-like bir egri icin 3 E1 uzayinda tanimlandi daha sonra, bu hareketin Darboux vektorleri [2] sabit ve hareketli uzaylar icin hesaplandi.

Research paper thumbnail of On Darboux Vectors of a Special Frenet Motion for a Time-Like Curve

A special Frenet motion with an one-parameter in 3 E has been given by Bottema [1]. In this study... more A special Frenet motion with an one-parameter in 3 E has been given by Bottema [1]. In this study, we give a generalization of [1] to 3 1 E , Minkowski 3-space. Firstly, this motion in 3 E is defined in 3 1 E for a time-like space curve and then Darboux vectors [2] of this motion is calculated for fixed and moving spaces in 3 1 E .

Research paper thumbnail of On 1-PARAMETER Motion in Lorentz Space 3 1 e

Bu calismada, bir α time-like egrisinin Darboux [2] vektorunden, Cayley formulu [1] yardimiyla, p... more Bu calismada, bir α time-like egrisinin Darboux [2] vektorunden, Cayley formulu [1] yardimiyla, pozitif semi ortogonal, A matrisi elde edildi. c =α alinarak x = Ax0 + c denklemiyle bir parametreli H / H′ Lorentziyan hareketi tanimlandi. Bu hareketin, Darboux vektorleri (matrisleri) bulundu. Daha sonra Darboux vektoru ile egrilikler matrisi arasindaki baginti verildi. Ayrica, Darboux vektorlerinin (matrislerinin) bilesenlerinin esit olmasi durumunda,α time-like egrisinin, bir genel helis olmasi gerektigi gosterildi.

Research paper thumbnail of On The Modified Orthogonal Frame with Curvature and Torsion in 3-Space

Mathematical Sciences and Applications E-Notes, 2016

In this paper, we study the modified orthogonal vector fields with curvature and torsion of a spa... more In this paper, we study the modified orthogonal vector fields with curvature and torsion of a space curve in Minkowski 3-Space.

Research paper thumbnail of On the rotation matrices in the semi-euclidean space

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 2006

Research paper thumbnail of Bıshop Frame of the Spacellike Curve With A Spacellike Principal Normal In Minkowski 3 Space

Research paper thumbnail of Homothetic motions at E 8 with cayley numbers

Mechanism and Machine Theory, 1995

In this paper, a matrix which is similar to Hamilton operators has been developed for Cayley numb... more In this paper, a matrix which is similar to Hamilton operators has been developed for Cayley numbers in eight dimensional Euclidean space E8 and a new motion has been defined by this matrix. It is shown that this is a homothetic motion. Furthermore, it has been found that the motion defined by regular curve of order r has only one

Research paper thumbnail of Bishop frame of the spacelike curve with a spacelike principal normal in Minkowski 3-space

Bu çalışmada, Bishop [1] tarafından yapılan çalışmayı, spacelike asli normalli spacelike eğriler ... more Bu çalışmada, Bishop [1] tarafından yapılan çalışmayı, spacelike asli normalli spacelike eğriler için Minkowski 3-uzayına genelleştirdik. İlaveten, spacelike eğriler için Bishop Darboux vektörü (matrisi) bulundu. Ayrıca, spacelike eğrinin T teğet vektörünün türevi kullanılarak, (K,\tau) ve (k_1,k_2) eğrilik fonksiyonları arasındaki ilişkiler bulundu.In this study, we generalize for a spacelike curve with a spacelike principal normal which was studied by Bishop [1] to Minkowski 3-Space. In addition, the Bishop Darboux vector (matrix) for spacelike curve is found. Furthermore, using the derivative of the tangent vector T of the spacelike curve, the relations between the curvature funtions K,\tau and k_1,k_2 is found

Research paper thumbnail of The Relation Between Base Curve of the Ruled Surface and It's Adjoint Curve

Research paper thumbnail of Sdü Fen Edebi̇yat Fakültesi̇ Fen Dergi̇si̇ (E-Dergi̇). 2008, 3(1), 80-90 Bishop Frame of the Timelike Curve in Minkowski 3-SPACE

In this study, we study the result which are obtained by BISHOP (1975) for a timelike curve in Mi... more In this study, we study the result which are obtained by BISHOP (1975) for a timelike curve in Minkowski 3-Space.In addition , the Darboux vector(matrix) for the timelike curve is found. Furthermore, using the derivative of the tangent vector T of the timelike curve, the relations between the curvature funtions τ κ , and 2 1 , k k are found.

Research paper thumbnail of New Characterizations For Bertrand Curves In Minkowski 3-Space

Bertrand curves have been investigated in Lorentzian and Minkowski spaces and some characterizati... more Bertrand curves have been investigated in Lorentzian and Minkowski spaces and some characterizations have been given in [1,2,6]. In this paper, we have investigated the relations between Frenet vector fields and curvatures and torsions of Bertrand curves at the corresponding points in Minkowski 3-space.

Research paper thumbnail of Minkowski 3-UZAYINDA Ti̇meli̇ke Eğri̇ni̇n Bi̇shop Çatisi

Biz bu calismada, BISHOP (1975) tarafindan elde edilen sonucu, Minkowski 3- uzayinda timelike egr... more Biz bu calismada, BISHOP (1975) tarafindan elde edilen sonucu, Minkowski 3- uzayinda timelike egriler icin calistik. Ilaveten, timelike egriler icin Darboux vectoru(matrisi) bulundu. Ayrica, timelike egrinin T teget vektorunun turevi kullanilarak κ,τ ve 1 2 k , k egrilik fonksiyonlari arasindaki iliskiler bulundu.

Research paper thumbnail of Ökli̇d Uzayinda Genel Cayley Dönüşümü Ve Dönme Matri̇sleri̇

Bu calismada, bir S anti-simetrik matrisi icin Cayley donusumu tanimlandi [1]. Anti-simetrik matr... more Bu calismada, bir S anti-simetrik matrisi icin Cayley donusumu tanimlandi [1]. Anti-simetrik matrislerle vektorler arasindaki bazi bagintilar verildi. Daha sonra, bir F donusumu tanimlandi. F donusu icin f (S) = I + S secildiginde, F(S) nin Cayley donusumune karsilik geldigi gosterildi. 2 f (S) = I − aS + bS secilme durumu da, Genel Cayley donusumu olarak adlandirildi. F(S) = A matrisinin pozitif ortogonal oldugu ve S ↔ s eksenini degismez biraktigi gosterildi. Boylece, F donusumunun s ekseni etrafinda belli bir donme yaptigi gosterildi. Ayrica 4 E , n E donme matrisleri belli sartlar altinda elde edildi ve iki Cayley matrisinin carpimina karsilik gelen eksen de bulundu.

Research paper thumbnail of E ’de TIME-LIKE BİR EĞRİ İÇİN ÖZEL BİR FRENET HAREKETİNİN DARBOUX VEKTÖRLERİ ÜZERİNE

Bir parametreli ozel Frenet hareketi, Bottema tarafindan 3-boyutlu Oklid uzayi E3 de verilmistir ... more Bir parametreli ozel Frenet hareketi, Bottema tarafindan 3-boyutlu Oklid uzayi E3 de verilmistir [1]. Bu calismada, E3 deki [1] Frenet hareketinin, 3 E1 , 3-boyutlu Minkowski uzayina bir genellestirilmesi veriliyor. Ilk olarak, E3 deki bu hareket, time-like bir egri icin 3 E1 uzayinda tanimlandi daha sonra, bu hareketin Darboux vektorleri [2] sabit ve hareketli uzaylar icin hesaplandi.

Research paper thumbnail of On Darboux Vectors of a Special Frenet Motion for a Time-Like Curve

A special Frenet motion with an one-parameter in 3 E has been given by Bottema [1]. In this study... more A special Frenet motion with an one-parameter in 3 E has been given by Bottema [1]. In this study, we give a generalization of [1] to 3 1 E , Minkowski 3-space. Firstly, this motion in 3 E is defined in 3 1 E for a time-like space curve and then Darboux vectors [2] of this motion is calculated for fixed and moving spaces in 3 1 E .

Research paper thumbnail of On 1-PARAMETER Motion in Lorentz Space 3 1 e

Bu calismada, bir α time-like egrisinin Darboux [2] vektorunden, Cayley formulu [1] yardimiyla, p... more Bu calismada, bir α time-like egrisinin Darboux [2] vektorunden, Cayley formulu [1] yardimiyla, pozitif semi ortogonal, A matrisi elde edildi. c =α alinarak x = Ax0 + c denklemiyle bir parametreli H / H′ Lorentziyan hareketi tanimlandi. Bu hareketin, Darboux vektorleri (matrisleri) bulundu. Daha sonra Darboux vektoru ile egrilikler matrisi arasindaki baginti verildi. Ayrica, Darboux vektorlerinin (matrislerinin) bilesenlerinin esit olmasi durumunda,α time-like egrisinin, bir genel helis olmasi gerektigi gosterildi.

Research paper thumbnail of On The Modified Orthogonal Frame with Curvature and Torsion in 3-Space

Mathematical Sciences and Applications E-Notes, 2016

In this paper, we study the modified orthogonal vector fields with curvature and torsion of a spa... more In this paper, we study the modified orthogonal vector fields with curvature and torsion of a space curve in Minkowski 3-Space.

Research paper thumbnail of On the rotation matrices in the semi-euclidean space

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 2006

Research paper thumbnail of Bıshop Frame of the Spacellike Curve With A Spacellike Principal Normal In Minkowski 3 Space

Research paper thumbnail of Homothetic motions at E 8 with cayley numbers

Mechanism and Machine Theory, 1995

In this paper, a matrix which is similar to Hamilton operators has been developed for Cayley numb... more In this paper, a matrix which is similar to Hamilton operators has been developed for Cayley numbers in eight dimensional Euclidean space E8 and a new motion has been defined by this matrix. It is shown that this is a homothetic motion. Furthermore, it has been found that the motion defined by regular curve of order r has only one