Marianty Ionel, McMaster University, October 28, 2002
Title: Second Order Families of Special Lagrangian 4-folds in C^4
Abstract:
In this talk I will discuss the problem of classifying the special
Lagrangian 4-folds in C^4, whose second fundamental form at a generic
point has a nontrivial SO(4)-stabilizer. These problem extends the
results of Robert Bryant who obtained a complete classification in
dimension 3.
Depending on the SO(4)-stabilizer G at a generic point of the fundamental
cubic of a special Lagrangian
4-fold, we get results such that there are no special Lagrangian 4-folds
whose fundamental cubic has stabilizer G or we get families of special
Lagrangian submanifolds that had already appeared in dimension 3 or even
new examples of families of special Lagrangian 4-folds.