Dual Quaternions and Dual Quaternionic Curves

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Dağdeviren A., Yüce S.

FILOMAT, vol.33, no.4, pp.1037-1046, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.2298/fil1904037d
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1037-1046
  • Yıldız Technical University Affiliated: Yes


After a brief review of the different types of quaternions, we develop a new perspective for dual quaternions with dividing two parts. Due to this new perspective, we will define the isotropic and non-isotropic dual quaternions. Then we will also give the basic algebraic concepts about the dual quaternions. Moreover, we define isotropic dual quaternionic curves and non-isotropic dual quaternionic curves. Via these definitions we find Serret-Frenet formulae for isotropic dual quaternionic curves. Finally, we will use these results to derive the Serret-Frenet formulae for non-isotropic dual quaternionic curves.