Title | Flat pencils of metrics and Frobenius manifolds |
Publication Type | Book Chapter |
Year of Publication | 1997 |
Authors | Dubrovin, B |
Book Title | Integrable systems and algebraic geometry : proceedings of the Taniguchi symposium 1997, Kobe, June 30 - July 4, 1997 and Research Institute for Mathematical Sciences, Kyoto University, July 7 - 11, 1997 / eds. M.-H. Saito, Y. Shimizu and K. Ueno. - Sing |
Series Volume | arXiv.org;math/9803106v1 |
Publisher | World Scientific |
ISBN Number | 981-02-3266-7 |
Abstract | 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. |
URL | http://hdl.handle.net/1963/3237 |
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