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Axes of Möbius Transformations in H3

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DOI: 10.4236/apm.2011.14038    4,311 Downloads   7,989 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

C. 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

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[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

  
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