22 March 2000.

Boris Kruglikov "Weyl tensors, compatibility of DE, geometric structures etc".

We consider overdetermined PDEs on 2-dimensional manifolds. We derive compatibility conditions by means of the Weyl tensor. For this we introduce higher Mayer brackets. We finish the exposition with an overview of other applications of the Weyl tensor, we consider geometric structures as PDEs and explain that in this case the Weyl tensor is Riemannian tensor in Riemannian geometry, Weyl tensor in conformal geometry, Weyl projective tensor in projective geometry, Nijenhuis tensor in almost complex geometry and others.