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Singularities of line congruences

Published online by Cambridge University Press:  12 July 2007

Shyuichi Izumiya ,
Kentaro Saji  and
Nobuko Takeuchi
Shyuichi Izumiya
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan (izumiya@math.sci.hokudai.ac.jp)
Kentaro Saji
Affiliation:
Department of Mathematics, Hiroshima University, Higashi Hiroshima 739-8526, Japan (sajik@hiroshima-u.ac.jp)
Nobuko Takeuchi
Affiliation:
Department of Mathematics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan (nobuko@u-gakugei.ac.jp)
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Abstract

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A line congruence is a two-parameter family of lines in R3. In this paper we study singularities of line congruences. We show that generic singularities of general line congruences are the same as those of stable mappings between three-dimensional manifolds. Moreover, we also study singularities of normal congruences and equiaffine normal congruences from the viewpoint of the theory of Lagrangian singularities.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 6 , December 2003 , pp. 1341 - 1359
Copyright
Copyright © Royal Society of Edinburgh 2003