F-manifolds with flat structure and Dubrovin's duality

By Yuri I. Manin. 2004

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This work continues the study of $F$--manifolds $(M,\circ)$, first defined by Hertling and Manin and investigated in [He]. The notion of a compatible flat structure $\nabla$ is introduced, and it is shown that many constructions known for Frobenius manifolds do not in fact require invariant metrics and can be developed for all such triples $(M,\circ ,\nabla).$ In particular, we extend and generalize recent Dubrovin's duality.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/de9a2261d13c8c0ae2934e88b303e09c22b003c7