Some remarks on associative submanifolds

Robert Bryant
Duke University

Many of the properties enjoyed
by special Lagrangian 3-folds in 3-dimensional
Calabi-Yau manifolds have analogs for associative
submanifolds in G2 manifolds. I will discuss some
of these properties, especially properties that
allow us to partially integrate these equations.
Several of the reductions of the associative system
seem to share the features of known 'completely
integrable' systems of PDE and I will try to explain
what I understand about this so far.

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