  We discuss geometrical aspects of Toda Fields generalizing the links between
Liouville gravity and uniformization of Riemann surfaces of genus greater than
one. The framework is the interplay between the hermitian and the holomorphic
geometry of vector bundles on such Riemann surfaces. Pointing out how Toda
fields can be considered as equivalent to Higgs systems, we show how the theory
of Variations of Hodge Structures enters the game inducing local holomorphic
embeddings of Riemann surfaces into homogeneous spaces. The relations of such
constructions with previous realizations of $W_n$--geometries are briefly
discussed.

High Energy Physics - Theory