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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Publisher's URL: http://dx.doi.org/10.1016/j.difgeo.2003.10.001
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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| 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: | 0926-2245 |
| ISSN (Online): | 1872-6984 |
| Published Online: | 21 November 2003 |
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