Some characterizations of dual vector fields

Öz

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.

Anahtar Kelimeler

• Dual space,directional derivative

Kaynakça

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