Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 2, pp. 325333 (2008) 

Timelike quaternion frame of a nonlightlike curveM. Özdemir and A. A. ErginDepartment of Mathematics, Akdeniz University, 07058 Antalya, Turkey, email: mozdemir07@gmail.com email: aaergin@akdeniz.edu.trAbstract: 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 nonlightlike curve and we find a reformulation of Frenet's formulas of nonlightlike curves in terms of the timelike quaternions in the Minkowski 3space. Moreover, we do same things for the parallel transport frame. Keywords: split quaternion, Frenet formulas, nonlightlike curves Classification (MSC2000): 53B30, 53A04, 15A66 Full text of the article:
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