Avviso di seminario: A system of PDE for calibrated submanifolds
[Aggiornamento: il seminario inizialmente previsto per giovedì 10 giugno è stato spostato a venerdì 11 giugno.]
Il giorno venerdì 11 giugno 2010 alle ore 11.00 nella sala conferenze "F.Tricerri" la prof.ssa Colleen Robles, Texas A&M Univ., terrà una conferenza dal titolo
"A system of PDE for calibrated submanifolds"
Abstract: A calibration on a Riemannian manifold $(M,g)$ is a closed $p$-form $\phi$ with the property that, when restricted to a tangent $p$-plane, $\phi \le \mathrm{vol}_g$. A $p$-dimensional submanifold $N$ of $M$ is calibrated if equality holds on the tangent spaces of $N$.
The closed calibrated submanifolds are global minimizers of volume in their homology class. For this reason, calibrations are a valuable tool in the study of minimal submanifolds. More generally, one may consider the $\phi$-critical submanifolds of $M$. These submanifolds include the calibrated submanifolds and, as I will show, are often minimal submanifolds of $M$.
In the case that $\phi$ is parallel, I will present an exterior differential system whose integral manifolds are precisely the $\phi$-critical submanifolds. The system generalizes the familiar characterizations by EDS of some of our favorite calibrated submanifolds, including the special Lagrangian, (co)associative and Cayley submanifolds.