  We consider the sigma models where the base metric is proportional to the
metric of the configuration space. We show that the corresponding sigma model
equation admits a Lax pair. We also show that this type of sigma models in two
dimensions are intimately related to the minimal surfaces in a flat pseudo
Riemannian 3-space. We define two dimensional surfaces conformally related to
the minimal surfaces in flat three dimensional geometries which enable us to
give a construction of the metrics of some even dimensional Ricci flat pseudo
Riemannian geometries.
