Gavin Ball, Jesse Madnick
Published 2019-09-17Version 1
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.
Comments: 37 pages. Section 2 of this preprint contains material from version 1 of our preprint arXiv:1905.03713. A new version of that preprint (1905.03713) will appear shortly to remove overlap
The Mean Curvature of First-Order Submanifolds in Geometries with Torsion
Intrinsic torsion and scalar curvature of Spin(7)-structure
Embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere
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