00967nas a2200121   4500008004300000020001800043245005200061210005200113260002100165520060300186100002000789856003600809       1997                        en_Ud    a981-02-3266-700aFlat pencils of metrics and Frobenius manifolds0 aFlat pencils of metrics and Frobenius manifolds  bWorld Scientific3 aThis 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.1 aDubrovin, Boris  uhttp://hdl.handle.net/1963/3237