Critical metrics for eigenvalues in Riemannian Geometry and minimal / harmonic maps

Eigenvalues of a differential operator defined using a metric (Laplace
operator, Dirac operator etc) are functionals on the space of Riemannian
metrics. Investigation of critical metrics for these functionals is a
natural approach in study of maximal / minimal metrics. It turns out that a
relation between critical metrics and minimal / harmonic maps is a very
powerful tool.