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

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arxiv 1909.08119 v1 pith:TYJPR6BT submitted 2019-09-17 math.DG

Gavin Ball , Jesse Madnick This is my paper · ORCID
classification math.DG
keywords foldscoassociativefoldtorsionassociativecayleycurvatureg2-structures
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We derive formulas for the mean curvature of associative 3-folds, coassociative 4-folds, and Cayley 4-folds in the general case where the ambient space has intrinsic torsion. Consequently, we are able to characterize those G2-structures (resp., Spin(7)-structures) for which every associative 3-fold (resp. coassociative 4-fold, Cayley 4-fold) is a minimal submanifold. In the process, we obtain new obstructions to the local existence of coassociative 4-folds in G2-structures with torsion.

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