Axes of Möbius Transformations in H3

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DOI: 10.4236/apm.2011.14038   PDF   HTML     4,536 Downloads   8,235 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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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