Evolution Equations for Special Lagrangian 3-Folds in C3 View Full Text


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Article Info

DATE

2001-11

AUTHORS

Dominic D. Joyce

ABSTRACT

This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in Cm. The previous paper (Math. Ann.320 (2001), 757–797), defined the idea of evolution data, which includes an (m − 1)-submanifold P in Rn, and constructed a family of special Lagrangian m-folds N in Cm, which are swept out by the image of P under a 1-parameter family of affine maps φt: Rn→ Cm, satisfying a first-order o.d.e. in t. In this paper we use the same idea to construct special Lagrangian 3-folds in C3. We find a one-to-one 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 C3.Our main results are a number of new families of special Lagrangian 3-foldsin C3, which we write very explicitly in parametric form. Generically these are nonsingular as immersed 3-submanifolds, and diffeomorphic to R3 or 1× R2. 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 ofcompact special Lagrangian 3-folds in Calabi–Yau 3-folds. This will beimportant in resolving the SYZ conjecture in Mirror Symmetry. More... »

PAGES

345-403

References to SciGraph publications

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URI

http://scigraph.springernature.com/pub.10.1023/a:1013034620426

DOI

http://dx.doi.org/10.1023/a:1013034620426

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1035493644


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