ONE-PARAMETER HOMOTHETIC MOTION IN THE MINKOWSKI 3-SPACE

Year 2016, Volume: 6 Issue: 1, 87 - 94, 01.06.2016

M. Jafari Y. Yaylı

Abstract

A one-parameter homothetic motion in three-dimensional Minkowski spaceis dened by means of the Hamilton operators. We study some properties of this motionand show that it has only one pole point at every instant t: We also obtain the Darbouxvector of the homothetic motion in E3 1 and show that it can be written as multiplicationof two split quaternions.

Keywords

Split quaternion , Hamilton operator , Homothetic motion , pole point

References

• Kula,L. and Yayli,Y., (2005), Homothetic motions in semi-Euclidean space E2, Mathematical Proceed- ings of the Royal Irish Academy, 105 A1, pp. 9-15.
• Kula,L. and Yayli,Y., (2007), Split quaternions and rotations in semi-Euclidean space E42, Journal of the Korean Mathematical Society, 44(6), pp. 1313-1327.
• Jafari,M. and Yayli,Y., (2014), Matrix Theory over the Split Quaternions, International journal of geometry, 3(2).
• Jafari,M., (2014), Homothetic motions in Euclidean 3-space, Kuwait journal of science, Vol. 41(1), pp. 65-73.
• Ozdemir,M. and Ergin,A.A., (2006), Rotation with unit timelike quaternions in Minkowski 3-space, Journal of Geometry and Physics, 56, pp. 322-336.
• Tosun,M., Kucuk,A. and Gungor,M.A., (2006), The Homothetic Motions in the Lorentz 3-space, Acta Mathematica Scientia, 26B(4), pp. 711-719.
• Yayli,Y., (1988), Hamilton operators and Lie groups, Ph.D. thesis, Gazi University, Ankara, Turkey.