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A New Representation of Canal Surfaces with Split Quaternions in Minkowski 3-Space

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Abstract

In this paper, we introduce canal surfaces determined by spherical indicatrices of any spatial curve in Minkowski 3-space by means of timelike split quaternions. Moreover, using orthogonal matrices corresponding to these quaternions, the canal surfaces are obtained as homotetic motions. Then, we investigate a relationship between the canal surfaces and unit split quaternions. Finally, we present some interesting examples with figures.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ankara University, Tandogan, Ankara, Turkey

    Erdem Kocakuşaklı, O. Oğulcan Tuncer, İsmail Gök & Yusuf Yaylı

Authors
  1. Erdem Kocakuşaklı
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  2. O. Oğulcan Tuncer
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  3. İsmail Gök
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  4. Yusuf Yaylı
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Correspondence to O. Oğulcan Tuncer.

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Kocakuşaklı, E., Tuncer, O.O., Gök, İ. et al. A New Representation of Canal Surfaces with Split Quaternions in Minkowski 3-Space. Adv. Appl. Clifford Algebras 27, 1387–1409 (2017). https://doi.org/10.1007/s00006-016-0723-5

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