turkmath.org

In this talk, an autonomous dynamical system on a two-dimensional manifold $M$ will be identified with an exterior differential system $\left(\Sigma,\mathcal{I}\right)$, where $\Sigma$ is a three-dimensional Riemannian manifold in $\mathbb{R}\times TM\simeq J^1(\mathbb{R},M)$ and $\mathcal{I}$ is the Pfaffian system generated by the contact forms on $\Sigma$. We will show that it is possible to construct a minimal but not necessarily totally geodesic surface in $\Sigma$ characterized by the corresponding dynamical system. As a particular case, a nontrivial minimal surface in the Heisenberg group will be discussed.