Osman ÇAKIR, SÜLEYMAN ŞENYURT

Differential Equations for a Space Curve According to the Unit Darboux Vector

ISSN: 2148-1830
Yayın Aralığı: 2
Başlangıç: 2013
Yayıncı: MATEMATİKÇİLER DERNEĞİ

In this work, the differential equation of a differentiable curve is expressed, by making use of Laplace and normal Laplace operators, as a linear combination of the unit Darboux vector defined as C = sinφT + cosφB of that curve. Later, the necessary and sufficient conditions are given for the space curves to be a 1-type Darboux vector.

Keywords:

Darboux vector, Laplacian operator,

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Alfred, G., Modern Differential Geometry of Curves and Surfaces with Mathematica, Boca Raton, Florida, USA: 2nd ed, CRC Press, 1997.
Arslan, K., Kocayigit, H., Onder, M., Characterizations of space curves with 1-type Darboux instantaneous rotation vector, CommunKorean Math. Soc., 31(2)(2016), 379–388.
Chen, B.Y., Ishikawa, S., Biharmonic surface in pseudo-Euclidean spaces, Mem Fac Sci Kyushu Univ Ser A, 45(2)(1991), 323–347.
Fenchel, W., On the differential geometry of closed space curves, Bull Amer Math Soc, 57(1951), 44–54.
Ferrandez, A., Lucas, P., Merano, MA., Biharmonic Hopf cylinders, Rocky Mountain J of Math, 28(3)(1998), 957–975.
Ferus, D., Schirrmacher, S., Submanifolds in Euclidean space with simple geodesics, Math Ann., 260(1982), 57–62.
Kocayigit, H., Hacisalihoglu, H.H., 1-type and biharmonic Frenet curves in Lorentzian 3-space, Iran J Sci Tech Trans A Sci, 33(2)(2009),159-168.
Kocayigit, H., Hacisalihoglu, H.H., 1-type and biharmonic curves in Euclidean 3-space, Int Electron J Geom, 4(1)(2011), 97–101.
Struik, D.J., Lectures on Classical Differential Geometry, Dover, GB: 2nd ed, Addison Wesley, 1988.