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David, Liana; Strachan, Ian A.B. (2011)
Publisher: Elsevier
Journal: Advances in Mathematics
Languages: English
Types: Article
Subjects: Mathematics(all), Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematics - Differential Geometry

Classified by OpenAIRE into

arxiv: Mathematics::Differential Geometry, Mathematics::Symplectic Geometry
A vector field E on an F-manifold (M, o, e) is an eventual identity if it is invertible and the multiplication X*Y := X o Y o E^{-1} defines a new F-manifold structure on M. We give a characterization of such eventual identities, this being a problem raised by Manin. We develop a duality between F-manifolds with eventual identities and we show that is compatible with the local irreducible decomposition of F-manifolds and preserves the class of Riemannian F-manifolds. We find necessary and sufficient conditions on the eventual identity which insure that harmonic Higgs bundles and DChk-structures are preserved by our duality. We use eventual identities to construct compatible pair of metrics.
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