On isoclinal sequences of spheres
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- by Asia Ivić Weiss PDF
- Proc. Amer. Math. Soc. 88 (1983), 665-671 Request permission
Abstract:
In $n$-dimensional inversive geometry it is possible to construct an infinite sequence of $(n - 1)$-spheres with the property that every $n + 2$ consecutive numbers are isoclinal. For every such sequence there is a Möbius transformation which advances the spheres of the sequence by one.References
- H. S. M. Coxeter, Loxodromic sequences of tangent spheres, Aequationes Math. 1 (1968), 104–121. MR 235456, DOI 10.1007/BF01817563
- Leon Gerber, Sequences of isoclinal spheres, Aequationes Math. 17 (1978), no. 1, 53–72. MR 493744, DOI 10.1007/BF01818539
- J. G. Mauldon, Sets of equally inclined spheres, Canadian J. Math. 14 (1962), 509–516. MR 142031, DOI 10.4153/CJM-1962-042-6 A. Weiss, On Coxeter’s loxodromic sequences of tangent spheres, The Geometric Vein, Springer-Verlag, Berlin and New York, 1982.
- J. B. Wilker, Inversive geometry, The geometric vein, Springer, New York-Berlin, 1981, pp. 379–442. MR 661793 —, Möbius transformations in dimension $n$, Period. Math. Hungar. (to appear).
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 665-671
- MSC: Primary 51B10; Secondary 51N25
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702296-5
- MathSciNet review: 702296