| Abstract: |
| The study of special holonomy involves a nonlinear second-order operator on differential forms called the G$_2$-Laplacian. In the first half of the talk, we will discuss a formula linking this operator to a natural Hodge Laplacian on a hypersurface. This result bears intriguing resemblance to the Gauss--Codazzi equation for the scalar curvature. In the second half, we will explain how our formula provides an integrability condition for the Poisson equation associated with the G$_2$-Laplacian in the presence of cohomogeneity one symmetry. Joint work with Timothy Buttsworth (The University of New South Wales) and Stepan Hudecek (The University of Queensland). |
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