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.