ジャイロベクトル空間
A. A. Ungar (2009). Gyrovectors: an Approach to Hyperbolic Geometry. Synthesis lectures on mathematics and statistics. Morgan & Claypool Publishers. ISBN 159-829-822-4. https://books.google.com/books?id=dlFTgrhqm3IC&pg=PR12&lpg=PR12&dq=gyrovectors+an+approach+to+hyperbolic+geometry#v=onepage&q=gyrovectors%20an%20approach%20to%20hyperbolic%20geometry&f=false
T. M. Rassias (2000). Mathematical Analysis and Applications. Collection of Articles in Mathematics. Hadronic Press. pp. 307, 326, 336. ISBN 157-485-045-8. https://books.google.com/books?id=rhjvAAAAMAAJ&q=gyrovector&dq=gyrovector
Maks A. Akivis And Vladislav V. Goldberg (2006), Local Algebras Of A Differential Quasigroup, Bulletin AMS, Volume 43, Number 2
双曲幾何学における固有速度空間モデルは、固有速度に以下の固有速度加算公式を加えることで与えられる。
u ⊕ U v = u + v + { β u 1 + β u u ⋅ v c 2 + 1 − β v β v } u {\displaystyle \mathbf {u} \oplus _{U}\mathbf {v} =\mathbf {u} +\mathbf {v} +\left\{{\frac {\beta _{\mathbf {u} }}{1+\beta _{\mathbf {u} }}}{\frac {\mathbf {u} \cdot \mathbf {v} }{c^{2}}}+{\frac {1-\beta _{\mathbf {v} }}{\beta _{\mathbf {v} }}}\right\}\mathbf {u} }