Hostname: page-component-7b9c58cd5d-7g5wt Total loading time: 0 Render date: 2025-03-15T05:18:52.356Z Has data issue: false hasContentIssue false

Singularities of line congruences

Published online by Cambridge University Press:  12 July 2007

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)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Copyright
Copyright © Royal Society of Edinburgh 2003