Families of surfaces and conjugate curve congruences
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Ana Claudia Nabarro
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 = M0 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 Cα0,0 and the way they bifurcate in the family Cα,t, with (α, t) close to (α0, 0).
© de Gruyter 2009
Articles in the same Issue
- Tropical invariants from the secondary fan
- Quotients of projective spaces and spheres
- Gauss curvature flow on surfaces of revolution
- Stringy E-functions of hypersurfaces and of Brieskorn singularities
- Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
- The classification of surfaces with pg = q = 1 isogenous to a product of curves
- Some quasihomogeneous Legendrian varieties
- Families of surfaces and conjugate curve congruences
Articles in the same Issue
- Tropical invariants from the secondary fan
- Quotients of projective spaces and spheres
- Gauss curvature flow on surfaces of revolution
- Stringy E-functions of hypersurfaces and of Brieskorn singularities
- Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
- The classification of surfaces with pg = q = 1 isogenous to a product of curves
- Some quasihomogeneous Legendrian varieties
- Families of surfaces and conjugate curve congruences
