HOMOTHETIC MOTIONS AND BICOMPLEX NUMBERS

Year 2009, Volume: 58 Issue: 1, 23 - 28, 01.02.2009

Faik Babadağ Yusuf Yaylı Nejat Ekmekçi

https://doi.org/10.1501/Commua1_0000000644

Abstract

In this study, one of the concepts of conjugate which is defined[1] for bicomplex numbers is investigated. In this case, the metric, in fourdimensional semi-Euclidean space E, has been defined by the help of theconcept of the conjugate.We define a motion in E2with the help of themetric in bicomplex numbers. We show that the motions de…ned by a curvelying on a hypersurface M of Eare homothetic motions . Furthermore, it isshown that the motion defined by a regular curve of order r and derivationsof the curve on the hypersurface M has only one acceleration centre of order(r-1) at every t- instant

Keywords

Bicomplex number, Homothetic motion, Hypersurface, Pole points, 53A05, 53A17

References

• Dominic Rochon and S.Tremblay, Bicomplex Quantum Mechanics: II. The Hilbert Space Adv. appl. Cliğord alg. DOI 10.1007/s00006-003-0000 , Birkhauser Verlag Basel/Switzerland, (2006)
• Dominic Rochon and M. Shapiro, On algebraic properties of bicomplex and hyperbolic num- bers,Anal. Univ.Oradea,fasc.math.,vol.11,71-110 (2004).
• O.P. Agrawal, Hamilton Operators and Dual Number Quaternions in Spatial Kinematics, Mec-Mach Theory (22),569-575(1987).
• H.Kabadayı, Y.Yaylı , Homothetic motion at E4with bicomplex numbers, Applied Mathe- matics Letters (Submitted)
• Y. Yaylı, Homothetic motions at E, Mech. Mach Theory 27(3), 303-305 (1992).
• G.B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, Inc: New York. I (1)-44(1) . (1991).
• Barrett O’Neill Semi-Riemannian Geometry, Pure and Applied Mathematics, 103 .Academic Pres, Inc. [Harcourt Brace Jovanovich, Publishers] New York. (1983). Current address : Department of Mathematics, Faculty of Science, University of Ankara, Tan
• do¼gan, Ankara, TURKEY E-mail address : [e-mail],[e-mail]
• [e-mail]