The Mean Curvature of Special Lagrangian 3-folds in SU(3)-Structures with Torsion

Abstract We derive formulas for the mean curvature of special Lagrangian 3-folds in the general case where the ambient 6-manifold has intrinsic torsion. Consequently, we are able to characterize those SU ( 3 ) -structures for which every special Lagrangian 3-fold is a minimal submanifold. In the process, we obtain an obstruction to the local existence of special Lagrangian 3-folds.