F-manifolds with flat structure and Dubrovin's duality

Abstract

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.

22 pages

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