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4 papers
Quadratic closed G2-structures
Gavin Ball
This article studies closed G2-structures satisfying the quadratic condition, a second-order PDE system introduced by Bryant involving a parameter For certain special values o…
Associative Submanifolds of the Berger Space
Gavin Ball, Jesse Madnick
We study associative submanifolds of the Berger space SO(5)/SO(3) endowed with its homogeneous nearly-parallel G2-structure. We focus on two geometrically interesting classes: the…
Closed G2-structures with conformally flat metric
Gavin Ball
This article classifies closed G2-structures such that the induced metric is conformally flat. It is shown that any closed G2-structure with conformally flat metric is locally equi…
The Mean Curvature of First-Order Submanifolds in Exceptional Geometries with Torsion
Gavin Ball, Jesse Madnick
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. Conse…