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Distributivity on the Gyrovector Spaces
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As a vector space provides a fundamental tool for the study of Euclideangeometry, a gyrovector space provides an algebraic tool for the study of hyperbolic ge-ometry. In general, the gyrovector spaces do not satisfy the distributivity with scalarmultiplication. In this article, we see under what condition the distributivity with scalarmultiplication is satisfied.
Abstract
As a vector space provides a fundamental tool for the study of Euclideangeometry, a gyrovector space provides an algebraic tool for the study of hyperbolic ge-ometry. In general, the gyrovector spaces do not satisfy the distributivity with scalarmultiplication. In this article, we see under what condition the distributivity with scalarmultiplication is satisfied.
참고문헌 (2)
- L. V. Sabinin., "On the notion of a gyrogroup", Aequ. Math, 56, pp.11~17 (1998)
- A. A. Ungar, "Analytic hyperbolic geometry and Albert Einstein's special theory of relativity" (2008), World Scienti c Press
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