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Ruled Surfaces in Minkowski 3-space and Split Quaternion Operators

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Abstract

In this paper, we define and classify split quaternion operators. Then, we show that the split quaternion product of a split quaternion operator and a curve, which lies on Lorentzian unit sphere or on hyperbolic unit sphere, parametrizes a ruled surface in the 3-dimensional Minkowski space \(\mathbb {E}_{1}^{3}\) if the vector part of the operator is perpendicular to the position vector of the spherical curve. Moreover, the ruled surfaces are represented as 2-parameter homothetic motions in \(\mathbb {E}_{1}^{3}\) by using semi-orthogonal matrices corresponding to the split quaternion operators. Finally, some examples are given to illustrate some applications of our main results.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, Ankara University, Tandoğan, 06100,, Ankara, Turkey

    Selahattin Aslan & Yusuf Yaylı

  2. Faculty of Education, Department of Mathematics Education, Gazi University, Ankara, 06500, Turkey

    Murat Bekar

Authors
  1. Selahattin Aslan
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  2. Murat Bekar
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  3. Yusuf Yaylı
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Correspondence to Selahattin Aslan.

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Communicated by Rafał Abłamowicz.

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Aslan, S., Bekar, M. & Yaylı, Y. Ruled Surfaces in Minkowski 3-space and Split Quaternion Operators. Adv. Appl. Clifford Algebras 31, 74 (2021). https://doi.org/10.1007/s00006-021-01176-x

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