SLANT HELICES IN MINKOWSKI SPACE <수식>
2
조회
0
다운로드
5
인용
0
참고문헌
키워드
초록
We consider a curve α = α(s) in Minkowski 3-space <수식> and denote by {T, N, B} the Frenet frame of α. We say that α is a slant helix if there exists a xed direction U of <수식> such that the function <N(s), U> is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of α. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in <수식>.
Abstract
We consider a curve α = α(s) in Minkowski 3-space <수식> and denote by {T, N, B} the Frenet frame of α. We say that α is a slant helix if there exists a xed direction U of <수식> such that the function <N(s), U> is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of α. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in <수식>.
참고문헌 (10)
- M. do Carmo, "Differential Geometry of Curves and Surfaces" (1976), Prentice Hall
- A. Ferrandez, "Null helices in Lorentzian space forms", Internat. J. Modern Phys. A, 16(30), pp.4845~4863 (2001)
- S. Izumiya, "New special curves and developable surfaces", Turkish J. Math, 28(2), pp.153~163 (2004)
- H. Kocayigit, "Timelike curves of constant slope in Minkowski space E4 1", J. Science Techn, 1, pp.311~318 (2007), Beykent Univ
- W. Kuhnel, "Differential Geometry: Curves, Surfaces, Manifolds" (1999), Braunschweig
- L. Kula, "On slant helix and its spherical indicatrix", Appl. Math. Comput, 169(1), pp.600~607 (2005)
- R. Lopez, "Differential geometry of curves and surfaces in Lorentz-Minkowski space", arXiv:0810.3351v1, ~ (2008)
- M.Onder, "B2-slant helix in Euclidean 4-space E4", Int. J. Contemp. Math. Sci, 3(29), pp.1433~1440 (2008)
- M. Petrovic-Torgasev, "W-curves in Minkowski space-time", Novi Sad J. Math, 32(2), pp.55~65 (2002)
- J. Walrave, "Curves and surfaces in Minkowski space", 박사, pp.1995