The Mean Curvature of First-Order Submanifolds in Geometries with Torsion

Gavin Ball, Jesse Madnick

Published 2019-05-09Version 1

We derive formulas for the mean curvature of special Lagrangian 3-folds, associative 3-folds, and coassociative 4-folds in the general case where the ambient space has intrinsic torsion. Consequently, we are able to characterize those SU(3)-structures (resp., G2-structures) for which every special Lagrangian 3-fold (resp. associative 3-fold, coassociative 4-fold) is a minimal submanifold. In the process, we obtain obstructions to the local existence of special Lagrangian 3-folds and coassociative 4-folds in manifolds with torsion.