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The existence of bitangent spheres

Published online by Cambridge University Press:  14 November 2011

Duan Hai-bao  and
Elmer Rees
Duan Hai-bao
Affiliation:
Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China
Elmer Rees
Affiliation:
Department of Mathematics, University of Edinburgh, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland
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Synopsis

Given any point x on a smooth, closed submanifold M of Euclidean space, there is a bitangent hyperplane or sphere that is tangent to M at x.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 1-2 , 1989 , pp. 85 - 87
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Bruce, J. W., Giblin, P. J. and Gibson, C. G.. Symmetry sets. Proc. Roy. Soc. Edinburgh Sect. A 101 (1985), 163–186.CrossRefGoogle Scholar
2Fomenko, A. T.Differential Geometry and Topology (New York: Consultants Bureau, 1987).Google Scholar
3Giblin, P. J. and O'Shea, D.. The bitangent sphere problem. Amer. Math. Monthly (to appear).Google Scholar
4Milnor, J.. Morse Theory. Ann. of Math. Stud. 51 (Princeton: Princeton U.P., 1963).Google Scholar