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

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

“…More precisely, we obtain an explicit obstruction to the local existence of coassociative 4-folds. Analogous obstructions to the local existence of special Lagrangian 3-folds are obtained in [2].…”

“…The complex irreducible representations of SU(2) × SU(2) are exactly the tensor products V p ⊗ V q of irreducible SU(2)-representations for each factor. The complex irreducible representations of SU (2) are well known to be the spaces of homogeneous polynomials in two variables of fixed degree, V p = Sym p (C x, y ). Let V C p,q denote V p ⊗V q .…”

“…Abstractly, these two SO(4)-modules are isomorphic, as are their irreducible summands. By Schur's Lemma, there is a one-dimensional family of SO(4)-module isomorphisms (Λ 2 7…”