Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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QUATERNIONS AND HOMOTHETIC MOTIONS IN EUCLIDEAN AND LORENTZIAN SPACES

  • Gulsum YUCA (Department of Mathematics, Aksaray University) ;
  • Yusuf YAYLI (Department of Mathematics, Ankara University)
  • Received : 2022.03.25
  • Accepted : 2023.02.02
  • Published : 2023.06.01
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Abstract

In the present paper, we investigate homothetic motions determined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable properties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.

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References

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