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Abstrakty
In this paper, we give some characterization for a osculating curve in 3-dimensional Euclidean space and we define a osculating curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement B1/1 of its first binormal vector field B1. In particular, we study the osculating curves in E4 and characterize such curves in terms of their curvature functions.
Wydawca
Czasopismo
Rocznik
Tom
Strony
931--939
Opis fizyczny
Bibliogr. 8 poz.
Twórcy
autor
autor
- Kirikkale University Faculty of Sciences and Arts Department of Mathematics Kirikkale, Turkey, kilarslan@yahoo.com
Bibliografia
- [1] B. Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110 (2003), 147-152.
- [2] B. Y. Chen, F. Dillen, Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Academia Sinica 33, No. 2 (2005), 77-90.
- [3] H. Gluck, Higher curvatures of curves in Euclidean space, Amer. Math. Monthly 73 (1966), 699-704.
- [4] W. Kuhnel, Differential Geometry: Curves-Surfaces-Manifolds, Braunschweig, Wiesbaden 1999.
- [5] R. S. Millman, G. D. Parker, Elements of Differential Geometry, Prentice-Hall, New Jersey 1977.
- [6] D. J. Struik, Differential Geometry, second ed., Addison-Wesley, Reading, Massachusetts 1961.
- [7] Y. C. Wong, On a explicit characterization of spherical curves, Proc. Amer. Math. Soc. 34 (1972), 239-242.
- [8] Y. C. Wong, A global formulation of the condition for a curve to lie in a sphere, Monats. Math.67 (1963), 363-365.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0023-0014