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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Lines tangent to $2n-2$ spheres in ${\mathbb R}^n$


Authors: Frank Sottile and Thorsten Theobald
Journal: Trans. Amer. Math. Soc. 354 (2002), 4815-4829
MSC (2000): Primary 14N10, 14P99, 51N20, 52A15, 68U05
Published electronically: June 5, 2002
MathSciNet review: 1926838
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that for $n \ge 3$there are $3 \cdot 2^{n-1}$ complex common tangent lines to $2n-2$ general spheres in $\mathbb{R}^n$ and that there is a choice of spheres with all common tangents real.


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Additional Information

Frank Sottile
Affiliation: Department of Mathematics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, Massachusetts 01003
Email: sottile@math.umass.edu

Thorsten Theobald
Affiliation: Zentrum Mathematik, Technische Universität München, München, Germany
Email: theobald@mathematik.tu-muenchen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03014-3
PII: S 0002-9947(02)03014-3
Received by editor(s): June 10, 2001
Received by editor(s) in revised form: October 29, 2001
Published electronically: June 5, 2002
Additional Notes: Research of first author supported in part by NSF grant DMS-0070494
Article copyright: © Copyright 2002 American Mathematical Society