Dubrovin's duality for $F$-manifolds with eventual identities
Differential Geometry
2020-12-15 v1 Exactly Solvable and Integrable Systems
Abstract
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.
Keywords
Cite
@article{arxiv.1006.0652,
title = {Dubrovin's duality for $F$-manifolds with eventual identities},
author = {Liana David and Ian A. B. Strachan},
journal= {arXiv preprint arXiv:1006.0652},
year = {2020}
}