Variational principles and moduli spaces

A key concept in Riemannian geometry is special holonomy. A particular instance of
this is provided by G2-manifolds which are 7-dimensional and carry a 3-form of
special algebraic type. This fundamental form induces a metric and is parallel with
respect to the associated Levi-Civita connection. We will interpret this is as an
Euler-Lagrange equation of a certain energy functional and show that the moduli
space of parallel forms is smooth. The talk is based on joint work with Hartmut Weiss.