Some characterizations of dual vector fields

Year 2016, Volume: 4 Issue: 3, 223 - 230, 30.09.2016

Hatice Kusak Samanci , Serkan Celik

Abstract

The set of the dual vectors which are introduced by ,  called as dual vector field. In our
paper, we introduce the directional derivative of the dual vector fields and
investigate some properties of them. Then we give a numeric example of the dual
vector field aided by E. Study theorem.

Keywords

Dual space, directional derivative

References

• Kandasamy, W.B.V., and Smarandache, F., Dual Numbers, Zip Publishing, Ohio, 2012.
• Study, E., Die Geometrie der Dynamen, Leibzig, 1903.
• Kazaz, M., Ozdemir, A., Ugurlu H.H., Eliptic Motion on Dual Hyperbolic Unit Sphere H ̃_0^2, Mechanism Machine Theory, 1450-1459, 2009.
• Veldkamp, G. R., On the Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mechanisms and Machine Theory, vol. 11 pp. 141-156, 1976.
• Taleshian, A., Application of Covariant Derivative in the Dual Space, Int. J. Contemp. Math. Sciences, Vol. 4, no. 17, 821-826, 2009.
• Ball, R.S., Theory of Screws, Cambridge University Press, Cambridge, 1900.
• O’Neill, B., Elementary Geometry Differential, New York and London, 1966.
• Do Carmo, M.P., Differential Geometry Curves and Surfaces, Prentice Hall, Englewood Cliffs, 1976.