Regular F -manifolds with eventual identities

Abstract

Given an F-manifold one may construct a dual multiplication (generalizing the idea of an almost-dual Frobenius manifold introduced by Dubrovin) using a so-called eventual identity, the definition of which ensure that the dual object is also an F-manifold. In this paper we solve the equations for an eventual identity for a regular (so non-semi-simple) F-manifold and construct a dual coordinate system in which dual multiplication is preserved. As an application, families of Nijenhuis operators are constructed.

24 pages

References in corpus (6)

• Dubrovin's duality for $F$-manifolds with eventual identities
• $F$-manifolds with eventual identities, bidifferential calculus and twisted Lenard-Magri chains
• F-manifolds and geometry of information
• Regular non-semisimple Dubrovin-Frobenius manifolds
• Symmetries of F-manifolds with eventual identities and special families of connections
• Integrable systems, Nijenhuis geometry and Lauricella bi-flat structures