Affiliation:
1. ICMC-USP, Dept. de Matemática, Av. do Trabalhador São-Carlense, 400 Centro, Caixa Postal 668, CEP 13560-970, São Carlos (SP), Brazil. Email:
2. Department of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom. Email:
Abstract
Abstract
Given a smooth and oriented surface M in the Euclidean space ℝ3, the conjugate curve congruence Cα
is a family of pairs of foliations on M that links the lines of curvature and the asymptotic curves of M. This family is first introduced in [Fletcher, Geometrical problems in computer vision, Liverpool University, 1996] and is studied in [Bruce, Fletcher, Tari, Contemp. Math. 354: 1–18, 2004, Bruce, Tari, Trans. Amer. Math. Soc. 357: 267–285, 2005]. When the surface M = M
0 is deformed in a 1-parameter family of surfaces Mt
, we obtain a 2-parameter family of conjugate curve congruence Cα,t
. We study in this paper the generic local singularities in C
α
0,0 and the way they bifurcate in the family Cα,t
, with (α, t) close to (α
0, 0).
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