Axes of Möbius Transformations in H3
Chang-Jun Li, Li-Jie Sun, Na Li
.
DOI: 10.4236/apm.2011.14038   PDF    HTML     4,954 Downloads   8,971 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.

Share and Cite:

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

[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

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.