• 호남수학학술지
• /
• 제46권1호
• /
• pp.101-113
• /
• 2024

In this paper, we define the generalized tricomplex numbers and give some algebraic properties of them. By using the matrix representation of generalized tricomplex numbers, we determine a motion on the hypersurface M in eight dimensional generalized linear space ℝ⁸_αβγ and show that this is a homothetic motion. Also, for some special cases of the real numbers α, β and γ, we give some examples of homothetic motions in ℝ⁸ and ℝ⁸₄ and obtain some rotational matrices in these spaces, too.

• 호남수학학술지
• /
• 제45권2호
• /
• pp.198-214
• /
• 2023

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.