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Focal Sets in Certain Riemannian Manifolds

Published online by Cambridge University Press:  20 January 2009

J. W. Bruce  and
D. J. Hurley
J. W. Bruce
Affiliation:
Department of MathematicsUniversity of Newcastle Upon Tyne
D. J. Hurley
Affiliation:
Department of MathematicsUniversity College, Corle, Eire
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In recent years the geometry of generic submanifolds of Euclidean space has been theobject of much study. Thorn hinted in [7] that the focal set of such a submanifold couldprofitably be studied by using the family of distance squared functions on thesubmanifold from points of the ambient space. For a generic submanifold the focal set isthe catastrophe or bifurcation set of this family. The key to obtaining results on thelocal structure of this focal set is a transversality theorem of Looijenga [5]; for analternative exposition see [8].

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 2 , June 1984 , pp. 209 - 214
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

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