Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 2, pp. 325-333 (2008)

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Timelike quaternion frame of a non-lightlike curve

M. Özdemir and A. A. Ergin

Department of Mathematics, Akdeniz University, 07058 Antalya, Turkey, e-mail: mozdemir07@gmail.com e-mail: aaergin@akdeniz.edu.tr

Abstract: A rotation matrix can be generated by a unit timelike quaternion in the three dimensional Minkowski space. In this paper, we correspond columns of this rotation matrix to Frenet vectors of a non-lightlike curve and we find a reformulation of Frenet's formulas of non-lightlike curves in terms of the timelike quaternions in the Minkowski 3-space. Moreover, we do same things for the parallel transport frame.

Keywords: split quaternion, Frenet formulas, non-lightlike curves

Classification (MSC2000): 53B30, 53A04, 15A66

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Electronic version published on: 18 Sep 2008. This page was last modified: 28 Jan 2013.

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