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Session S39 - Differential Equations and Geometric Structures

Tuesday, July 13, 14:00 ~ 14:50 UTC-3

The Double Eigenvalues Curve of a Line Congruence

Marcos Craizer

Pontifícia Universidade Católica do Rio de Janeiro, Brasil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A line conguence is a 2-dimensional arrangement of lines in 3-space. It is a classical topic of projective differential geometry and has many relations with binary differential equations. The curve where the principal directions coincide is called the double eigenvalues curve of the line congruence.

In this talk we classify the generic singularities of the focal surface along the double eigenvalues curve. A basic tool is the support function associated with an eq\"uiaffine vector field transversal to a surface in 3-space

Joint work with Ronaldo A. Garcia (Universidade Federal de Goiás, Brasil).

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