Some characterization of osculating curves in the Euclidean spaces

• Autorzy: Ilarslan K. , Nesovic E.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

osculating curve; curves; Frenet equation; Euclidean spaces

PL

krzywa ściśle styczna; krzywe; równanie Freneta; przestrzenie Euclidesowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 4
• Strony: 931--939
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Ilarslan K.

autor

Nesovic E.

• Kirikkale University Faculty of Sciences and Arts Department of Mathematics Kirikkale, Turkey,

Bibliografia

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• [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.