# On the structure of Lagrangian submanifolds

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Knut Smoczyk, Gottfried Wilhelm Leibniz Universität, Hannover
Fine Hall 314

This is a report on a recent joint project with Lars Schaefer. We derive results related to the minimality of Lagrangian submanifolds. In particular, these apply to Lagrangian 3-folds and to Lagrangian submanifolds in twistor spaces over quaternionic Kaehler manifolds. We then use a splitting theorem to give a better description in dimensions four and five.