Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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HOMOTHETIC MOTIONS WITH GENERALIZED TRICOMPLEX NUMBERS

  • Received : 2023.05.27
  • Accepted : 2023.07.16
  • Published : 2024.03.20
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Abstract

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 ℝ8αβγ 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.

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References

  1. F. Babadag, Y. Yayli, and N. Ekmekci, Homothetic motions at E8 with bicomplex numbers C3, Int. J. Contemp. Math. Sciences 4 (2009), no. 33-36, 1619-1626.
  2. F. Babadag, Y. Yayli, and N. Ekmekci, Homothetic motion and bicomplex numbers, Commun. Fac. Sci. Univ. Ank. Series A1 Math. Stat. 58 (2009), no. 1, 23-28.
  3. H. H. Hacisalihoglu, On the rolling of one curve or surface upon another, Proc. Roy. Irish Acad. Sect. 71 (1971), 13-17.
  4. M. Jafari and Y. Yayli, Homothetic motion at E4αβ, Int. J. Contemp. Math. Sci. 5 (2010), no. 45-48, 2319-2326.
  5. H. Kabadayi and Y. Yayli, Homothetic motions at E4 with bicomplex numbers, Adv. Appl. Clifford Algebra, 21 (2011), no. 3, 541-546. https://doi.org/10.1007/s00006-010-0266-0
  6. F. Kahraman Aksoyak and Y. Yayli Homothetic motions and Lie groups in ℝ42, J. Dyn. Syst. Geom. Theor. 11 (2013), no. 1-2, 23-38. https://doi.org/10.1080/1726037X.2013.823808
  7. F. Kahraman Aksoyak and Y. Yayli Homothetic motions and surfaces in E4, Bull. Malays. Math. Sci. Soc. 38 (2015), no. 1, 259-269. https://doi.org/10.1007/s40840-014-0017-9
  8. F. Kahraman Aksoyak and S. Ozkaldi Karakus, Homotetic motions via generalized bicomplex numbers, Facta Univ. Ser. Math. Inform 36 (2021), no. 2, 275-291.
  9. G. Ozaydin, Homothetic Motion with Generalized Bicomplex Numbers, Master Thesis, Bilecik Seyh Edebali University, Institute of Science, Bilecik, Turkey, 2019.
  10. S. Ozkaldi Karakus and F. Kahraman Aksoyak, Generalized bicomplex numbers and Lie groups, Adv. Appl. Clifford Algebra 25 (2015), no. 4, 943-963. https://doi.org/10.1007/s00006-015-0545-x
  11. S. Ozkaldi and Y. Yayli Tensor product surfaces in ℝ4 and Lie groups, Bull. Malays. Math. Sci. Soc. 33 (2010), no. 1, 69-77.
  12. S. Ozkaldi and Y. Yayli Bicomplex number and tensor product surfaces in ℝ42, Ukrainian Math. J. 64 (2012) no. 3, 344-355. https://doi.org/10.1007/s11253-012-0651-z
  13. G. B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Deccer, Inc., New York, 1990.
  14. C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann. 40 (1892), no. 3, 413-467. https://doi.org/10.1007/BF01443559
  15. Y. Yayli, Homothetic motion at E4, Mech. Mach. Theory 27 (1992), 303-305. https://doi.org/10.1016/0094-114X(92)90020-I
  16. Y. Yayli and B. Bukcu, Homothetic motions at E8 with Cayley numbers, Mech. Mach. Theory 30 (1995), 417-420. https://doi.org/10.1016/0094-114X(94)00037-L