This paper is based on the author's talk at 1997 Taniguchi Symposium
``Integrable Systems and Algebraic Geometry''. We consider an approach to the
theory of Frobenius manifolds based on the geometry of flat pencils of
contravariant metrics. It is shown that, under certain homogeneity assumptions,
these two objects are identical. The flat pencils of contravariant metrics on a
manifold M appear naturally in the classification of bihamiltonian structures
of hydrodynamics type on the loop space L(M). This elucidates the relations
between Frobenius manifolds and integrable hierarchies.Comment: 25 pages, no figures, plain Te
