Comments on Parallel Curves in 3-Dimensional Lie Group G

Ali Çakmak; Pelin Ezgi Epik

Makale detayları

Comments on Parallel Curves in 3-Dimensional Lie Group G

Yazarlar:

Ali Çakmak | Pelin Ezgi Epik

Yayıncı:

Bingol University

Ana Başlıklar:

Matematiksel Fizik (Diğer)

Dergi:

Türk Doğa ve Fen Dergisi Issue 1, pp.37-42

Belge Tipi:

Makale

Yayın Tarihi:

1/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001328979

pISSN:

2149-6366

Anahtar kelimeler:

Özet:

 In this study, firstly, basic concepts in 3-dimensional Euclidean space and basic information about curves are given and some special curves are examined. Then, basic information about Lie algebra and Lie group basic concepts and curves are given and special curves such as helix, involute-evolute, Bertrand, Mannheim, Smarandache, are defined. Secondly, inspired by these special curves examined in the Lie group, the definitions of the parallel curve in the vector direction, the parallel curve in the direction of the vector B and the parallel curve in the direction of the linear combination of the vectors B and N of a curve according to the Frenet frame are given and characterized. Some theorems and results are obtained by finding the Frenet apparatus of these characterized curves. Finally, the findings are examined in more specific circumstances and new results are found.

 In this study, firstly, basic concepts in 3-dimensional Euclidean space and basic information about curves are given and some special curves are examined. Then, basic information about Lie algebra and Lie group basic concepts and curves are given and special curves such as helix, involute-evolute, Bertrand, Mannheim, Smarandache, are defined. Secondly, inspired by these special curves examined in the Lie group, the definitions of the parallel curve in the vector direction, the parallel curve in the direction of the vector B and the parallel curve in the direction of the linear combination of the vectors B and N of a curve according to the Frenet frame are given and characterized. Some theorems and results are obtained by finding the Frenet apparatus of these characterized curves. Finally, the findings are examined in more specific circumstances and new results are found.

 In this study, firstly, basic concepts in 3-dimensional Euclidean space and basic information about curves are given and some special curves are examined. Then, basic information about Lie algebra and Lie group basic concepts and curves are given and special curves such as helix, involute-evolute, Bertrand, Mannheim, Smarandache, are defined. Secondly, inspired by these special curves examined in the Lie group, the definitions of the parallel curve in the vector direction, the parallel curve in the direction of the vector B and the parallel curve in the direction of the linear combination of the vectors B and N of a curve according to the Frenet frame are given and characterized. Some theorems and results are obtained by finding the Frenet apparatus of these characterized curves. Finally, the findings are examined in more specific circumstances and new results are found.

 In this study, firstly, basic concepts in 3-dimensional Euclidean space and basic information about curves are given and some special curves are examined. Then, basic information about Lie algebra and Lie group basic concepts and curves are given and special curves such as helix, involute-evolute, Bertrand, Mannheim, Smarandache, are defined. Secondly, inspired by these special curves examined in the Lie group, the definitions of the parallel curve in the vector direction, the parallel curve in the direction of the vector B and the parallel curve in the direction of the linear combination of the vectors B and N of a curve according to the Frenet frame are given and characterized. Some theorems and results are obtained by finding the Frenet apparatus of these characterized curves. Finally, the findings are examined in more specific circumstances and new results are found.

Makale detayları

Comments on Parallel Curves in 3-Dimensional Lie Group G

Yazarlar:

Ali Çakmak | Pelin Ezgi Epik

Yayıncı:

Bingol University

Ana Başlıklar:

Matematiksel Fizik (Diğer)

Dergi:

Türk Doğa ve Fen Dergisi Issue 1, pp.37-42

Belge Tipi:

Makale

Yayın Tarihi:

1/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001328979

pISSN:

2149-6366

Lie group

Parallel curve

Some special curves

Sayı

Makale detayları

Comments on Parallel Curves in 3-Dimensional Lie Group G

Yazarlar: Ali Çakmak | Pelin Ezgi Epik

Yayıncı: Bingol University

Ana Başlıklar: Matematiksel Fizik (Diğer)

Dergi: Türk Doğa ve Fen Dergisi Issue 1, pp.37-42

Belge Tipi: Makale

Yayın Tarihi: 1/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001328979

pISSN: 2149-6366

Lie group

Parallel curve

Some special curves

Sayı

Yazarlar:

Ali Çakmak | Pelin Ezgi Epik

Yayıncı:

Bingol University

Ana Başlıklar:

Matematiksel Fizik (Diğer)

Dergi:

Türk Doğa ve Fen Dergisi Issue 1, pp.37-42

Belge Tipi:

Makale

Yayın Tarihi:

1/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001328979

pISSN:

2149-6366