Evolution equations for special Lagrangian 3-folds in C^3

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dc.creatorJoyce, Dominic
dc.date2000-10-03
dc.date2001-08-01
dc.date.accessioned2026-07-07T04:37:49Z
dc.date.available2026-07-07T04:37:49Z
dc.descriptionThis is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The previous paper in the series, math.DG/0008155, defined the idea of evolution data, which includes an (m-1)-submanifold P in R^n, and constructed a family of special Lagrangian m-folds N in C^m, which are swept out by the image of P under a 1-parameter family of linear or affine maps phi_t : R^n -> C^m, satisfying a first-order o.d.e. in t. In this paper we use the same idea to construct special Lagrangian 3-folds in C^3. We find a 1-1 correspondence between sets of evolution data with m=3 and homogeneous symplectic 2-manifolds P. This enables us to write down several interesting sets of evolution data, and so to construct corresponding families of special Lagrangian 3-folds in C^3. Our main results are a number of new families of special Lagrangian 3-folds in C^3, which we write very explicitly in parametric form. Generically these are nonsingular as immersed 3-submanifolds, and diffeomorphic to R^3 or S^1 x R^2. Some of the 3-folds are singular, and we describe their singularities, which we believe are of a new kind. We hope these 3-folds will be helpful in understanding singularities of compact special Lagrangian 3-folds in Calabi-Yau 3-folds. This will be important in resolving the SYZ conjecture in Mirror Symmetry.
dc.description54 pages, LaTeX. (v2) references updated, minor corrections
dc.identifierhttps://arxiv.org/abs/math/0010036
dc.identifierhttp://arxiv.org/abs/math/0010036
dc.identifierAnnals of Global Analysis and Geometry 20 (2001), 345-403.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60048
dc.subjectDifferential Geometry
dc.titleEvolution equations for special Lagrangian 3-folds in C^3
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