ON THE BISHOP CURVATURES OF CURVES IN EUCLIDEAN SPACES
- Abstract
- In this thesis, we study the properties of curves in Euclidean space. Firstly we review the Frenet formulas in Euclidean space and Lorentz space, respectively. And we study the several curves with the Frenet theory. Also, we introduce the Bishop theory and study the relations between Frenet theory and Bishop theory.
본 논문에서는 유클리드 공간상의 곡선의 성질에 대해 연구하였다. 첫째로, 유클리드 공간과 로렌츠 공간 각각에서의 Frenet공식을 알아보았다. 그리고 Frenet이론과 함께 여러가지 곡선에 대해 알아보았다. 또한, Bishop 이론을 소개하고 Frenet이론과 Biship 이론 사이의 관계를 연구하였다.
- Issued Date
- 2010
- Awarded Date
- 2010. 2
- Type
- Dissertation
- Alternative Author(s)
- Kim, Hye Jung
- Affiliation
- 제주대학교 대학원
- Department
- 대학원 수학과
- Advisor
- 정승달
- Table Of Contents
- 1. Introduction 1
2. Curves in Rⁿ 2
2.1 Curves in Rⁿ 2
2.2 Euclidean isometry 4
3. Frenet formulas 7
3.1 Frenet formula in R3 7
3.2 The sphere curves 10
3.3 Bertrand curves 13
3.4 Involutes and Evolutes 15
3.5 Frenet formula in Minkowski space R³₁ 16
3.6 Frenet formula in Rⁿ 18
4. Bishop formulas 21
4.1 Bishop formula in R3 21
4.2 Bishop formula in Rⁿ 24
References 27
Abstract (Korean) 28
Acknowledgements (Korean) 29
- Degree
- Master
- Publisher
- 제주대학교 대학원
- Citation
- 김혜정. (2010). ON THE BISHOP CURVATURES OF CURVES IN EUCLIDEAN SPACES
- Appears in Collections:
- General Graduate School > Mathematics
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