The Mean Curvature of (Co)Associative Submanifolds

Geometry/topology Seminar

Jesse Madnick (McMaster University, Mathematics)

Monday, February 18, 2019 -
3:15pm to 4:15pm
Location: 
119 Physics

In flat R^7, two classes of submanifolds stand out: the associative 3-folds and coassociative 4-folds, which enjoy the remarkable property of being area-minimizing in their homology class. In fact, these submanifolds make sense in any 7-manifold with a G2-structure, and it is natural to ask: Under what conditions to do they continue to be minimal? We answer this question by deriving pleasantly simple formulas for their mean curvature. Time permitting, we will explain how these formulas suggest new avenues for the construction of minimal submanifolds of high codimension. This is joint work with Gavin Ball.

Last updated: 2019/02/20 - 10:25pm