Back
 APM  Vol.1 No.4 , July 2011
Axes of Möbius Transformations in H3
Chang-Jun Li, Li-Jie Sun, Na Li
Abstract: This paper gives the relationship between the positions of axes of the two nonparabolic elements that gener-ate a discrete group and these nature including the translation lengths along the axes and the rotation angles. we mainly research the intersecting position and the coplanar (but disjoint) position.
Keywords: Geodesic, Discrete, Axis
Cite this paper: nullC. Li, L. Sun and N. Li, "Axes of Möbius Transformations in H3," Advances in Pure Mathematics, Vol. 1 No. 4, 2011, pp. 218-220. doi: 10.4236/apm.2011.14038.
References

[1]   A. F. Beardon, “The Geometry of Discrete Groups,” Spring-Verlag, New York, 1983, p. 66.

[2]   C. Cao, “Some Trace Inequalities for Discrete Groups of M?bius Transforma-tions,” Proceedings of the American Mathematical Society, Vol. 123, No. 12, 1995, pp. 3807-3815. doi:10.2307/2161910

[3]   F. W. Gehring and G. J. Martin, “Commutators, Collars and the Geometry of M?bius Groups,” Journal d’Analyse Mathématique, Vol. 63, No. 1, 1994, pp. 175-219. doi:10.1007/BF03008423

[4]   F. W. Gehring and G. J. Martin, “Geodesics in Hyperbolic 3-Folds,” Michigan Mathematical Journal, Vol. 44, No. 2, 1997, pp. 331-343. doi:10.1307/mmj/1029005708

[5]   F. W. Gehring and G. J. Martin, “Inequalities for M?bius Transformations and Discrete Groups,” Journal für die Reine und Angewandte Mathematik, No. 418, 1991, pp. 31-76. doi:10.1515/crll.1991.418.31

 
 
Top