Sur la classification des hexagones hyperboliques à angles droits en dimension 5

François Delgove; Nicolas Retailleau

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 5, page 1049-1061
  • ISSN: 0240-2963

Abstract

top
The aim of this paper is to give a classification of the right-angled hyperbolic hexagons in the real hyperbolic space ℍ ℝ 5 , by using a quaternionic distance between geodesics in ℍ ℝ 5 .

How to cite

top

Delgove, François, and Retailleau, Nicolas. "Sur la classification des hexagones hyperboliques à angles droits en dimension 5." Annales de la faculté des sciences de Toulouse Mathématiques 23.5 (2014): 1049-1061. <http://eudml.org/doc/275407>.

@article{Delgove2014,
abstract = {The aim of this paper is to give a classification of the right-angled hyperbolic hexagons in the real hyperbolic space $\{\mathbb\{H\}\}_\{\{\mathbb\{R\}\}\}^\{5\}$, by using a quaternionic distance between geodesics in $\{\mathbb\{H\}\}_\{\{\mathbb\{R\}\}\}^\{5\}$.},
author = {Delgove, François, Retailleau, Nicolas},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {right-angled hexagon; real hyperbolic space; orientation-preserving isometry; Hamilton's quaternions; quaternionic distance; geodesic; cross-ratio; bi-ratio},
language = {eng},
number = {5},
pages = {1049-1061},
publisher = {Université Paul Sabatier, Toulouse},
title = {Sur la classification des hexagones hyperboliques à angles droits en dimension 5},
url = {http://eudml.org/doc/275407},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Delgove, François
AU - Retailleau, Nicolas
TI - Sur la classification des hexagones hyperboliques à angles droits en dimension 5
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 5
SP - 1049
EP - 1061
AB - The aim of this paper is to give a classification of the right-angled hyperbolic hexagons in the real hyperbolic space ${\mathbb{H}}_{{\mathbb{R}}}^{5}$, by using a quaternionic distance between geodesics in ${\mathbb{H}}_{{\mathbb{R}}}^{5}$.
LA - eng
KW - right-angled hexagon; real hyperbolic space; orientation-preserving isometry; Hamilton's quaternions; quaternionic distance; geodesic; cross-ratio; bi-ratio
UR - http://eudml.org/doc/275407
ER -

References

top
  1. Beardon (A. F.).— The geometry of discrete groups, Springer (1983). Zbl0528.30001MR698777
  2. Bisi (C.) and Gentili (G.).— Möbius transformations and the Poincaré distance in the quaternionic setting, Indiana Univ. Math. J., 350, p. 2729-2764 (2009). Zbl1193.30067MR2603766
  3. Bonahon (F.).— Low-dimensional geometry : from Euclidean surfaces to hyperbolic knots, Amer. Math. Soc. (2009). Zbl1176.57001MR2522946
  4. Dieudonné (J.).— Les déterminants sur un corps non commutatif, Bull. Soc. Math. France, 71, p. 27-45(1943). Zbl0028.33904MR12273
  5. Fathi (A.), Laudenbach (F.), and Poenaru (V.).— Travaux de Thurston sur les surfaces, Astérisque, vol. 66-67, Soc. Math. France. (1979). Zbl0446.57010MR568308
  6. Fenchel (W.).— Elementary geometry in hyperbolic space, de Gruyter (1989). Zbl0674.51001MR1004006
  7. Gwynne (E.) and Libine (M.).— On a quaternionic analogue of the cross-ratio, Adv. App. Clifford Algebra, 22, p. 1041-1053 (2012). Zbl1257.15014MR2994138
  8. Hellegouarch (Y.).— Quaternionic homographies : Application to Ford hyperspheres, Comptes-Rendus Acad. Science Canada, 11, p. 171-176 (1989). Zbl0711.51004MR1010923
  9. Parizet (J.).— Quaternions et géométrie. Notes de cours sur Internet, http :// www.math.unicaen.fr/lmno/semana/documents/parizet/Quaternions _ A.pdf. 
  10. Parker (J. R.).— Hyperbolic spaces, Jyväskylä Lect. in Math., 2 (2008). 
  11. Paulin (F.) and Parkkonen (J.).— Prescribing the behaviour of geodesics in negative curvature, Geom. & Topo., 14, p. 277-392 (2010). Zbl1191.53026MR2578306
  12. Paulin (F.) and Parkkonen (J.).— On the arithmetic and geometry of binary Hamiltonian forms, Alg. Numb. Theo., 7, p. 75-115 (2013). Zbl1273.11065MR3037891
  13. Perrin (D.).— Cours d’algèbre, Ellipses (1996). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.