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Frobenius Manifolds: Natural submanifolds and induced bi-Hamiltonian structures

I. A. B. Strachan
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Abstract

Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but will, in general, be curved. The induced curvature is studied, a main result being that these natural submanifolds carry a induced pencil of compatible metrics. It is then shown how one may constrain the bi-Hamiltonian hierarchies associated to a Frobenius manifold to live on these natural submanifolds whilst retaining their, now non-local, bi-Hamiltonian structure.

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BibTeXRIS

I. A. B. Strachan. 2002-01-07. Frobenius Manifolds: Natural submanifolds and induced bi-Hamiltonian structures. https://doi.org/10.1016/j.difgeo.2003.10.001

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