Frobenius manifolds: natural submanifolds and induced bi-Hamiltonian structures

Strachan, I.A.B. (2004) Frobenius manifolds: natural submanifolds and induced bi-Hamiltonian structures. Differential Geometry and its Applications, 20(1), pp. 67-99. (doi: 10.1016/j.difgeo.2003.10.001)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Strachan, Professor Ian
Authors: Strachan, I.A.B.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Differential Geometry and its Applications
ISSN (Online):1872-6984
Published Online:21 November 2003

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