Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Distributivity on the Gyrovector Spaces

  • Kim, Sejong (Department of Mathematics, Chungbuk National University)
  • Received : 2014.03.03
  • Accepted : 2014.07.14
  • Published : 2015.03.23
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Abstract

As a vector space provides a fundamental tool for the study of Euclidean geometry, a gyrovector space provides an algebraic tool for the study of hyperbolic geometry. In general, the gyrovector spaces do not satisfy the distributivity with scalar multiplication. In this article, we see under what condition the distributivity with scalar multiplication is satisfied.

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References

  1. L. V. Sabinin, L. L. Sabinin, and L. V. Sbitneva, On the notion of a gyrogroup, Aequ. Math., 56(1998), 11-17. https://doi.org/10.1007/s000100050039
  2. A. A. Ungar, Analytic hyperbolic geometry and Albert Einstein's special theory of relativity, World Scientific Press, 2008.