The hyperbolic derivative in the Poincaré ball model of hyperbolic geometry

@article{Birman2001TheHD,
  title={The hyperbolic derivative in the Poincar{\'e} ball model of hyperbolic geometry},
  author={Graciela Silvia Birman and Abraham Albert Ungar},
  journal={Journal of Mathematical Analysis and Applications},
  year={2001},
  volume={254},
  pages={321-333}
}
  • G. Birman, A. Ungar
  • Published 1 February 2001
  • Mathematics
  • Journal of Mathematical Analysis and Applications
The generic Mobius transformation of the complex open unit disc induces a binary operation in the disc, called the Mobius addition. Following its introduction, the extension of the Mobius addition to the ball of any real inner product space and the scalar multiplication that it admits are presented, as well as the resulting geodesics of the Poincare ball model of hyperbolic geometry. The Mobius gyrovector spaces that emerge provide the setting for the Poincare ball model of hyperbolic geometry… 

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