Special Lagrangian Cones in C3 and Primitive Harmonic Maps
By I. McIntosh. 2002
80 citations recorded by the source corpus.
It is shown that every special Lagrangian cone in C3 determines, and is determined by, a primitive harmonic surface in the 6‐symmetric space SU3/SO2. For cones over tori, this allows the classification theory of harmonic tori to be used to describe the construction of all the corresponding special Lagrangian cones. A parameter count is given for the space of these, and some of the examples found recently by Joyce are put into this context.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3366ddaf437d7bd5f8eb742bd26c3e98cbcd1472
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Minimal Lagrangian 2‐Tori in CP2 Come in Real Families of Every Dimension (2003, methodology): “1 2 EMMA CARBERRY AND IAN MCINTOSH [ 13 ] for details).”
- Special Lagrangian cones (2000, background): “For example, for tori both equations are in some sense integrable systems—the Sinh-Gordon equation for minimal tori in S3 and another integrable equation ∆u = eu − e−2u for minimal Legendrian tori in S5 (see [21] for details in the minimal Legendrian case).”
- The geometric complexity of special Lagrangian T2-cones (2003, methodology): “Recently a number of authors have used integrable systems techniques to prove existence of large numbers of such SLG cones [8,21,25, 42 ].”
- Lectures on special Lagrangian geometry (2001, background): “Many people have helped me develop my ideas on special Lagrangian geometry; amongst them I would particularly like to thank Robert Bryant, Mark Gross, Mark Haskins, Nigel Hitchin, Ian McIntosh, Richard Thomas, and Karen Uhlenbeck.”
- Special Lagrangian cones with higher genus links (2005, methodology): “Very recently, the existence of many more SLG cones over 2-tori in S 5 was proved using more sophisticated algebro-geometric tools from integrable systems [6, 40 ].”
- Survey on Affine Spheres (2008, methodology): “For example, see McIntosh [56] for an application of solutions to”
- Construction of Lagrangian Self-similar Solutions to the Mean Curvature Flow in $$\mathbb{C}^n$$ (2006, background): “In particular, we recover all self-shrinking planar curves, which were first found by Abresch and Langer [17] (see also [13]).”