Dubrovin's duality for F-manifolds with eventual identities

David, L. and Strachan, I. A.B. (2011) Dubrovin's duality for F-manifolds with eventual identities. Advances in Mathematics, 226(5), pp. 4031-4060. (doi: 10.1016/j.aim.2010.11.006)

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Publisher's URL: http://dx.doi.org/10.1016/j.aim.2010.11.006


A vector field <i>E</i> on an <i>F</i>-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 <i>M</i>. We give a characterization of such eventual identities, this being a problem raised by Manin. We develop a duality between <i>F</i>-manifolds with eventual identities and we show that is compatible with the local irreducible decomposition of <i>F</i>-manifolds and preserves the class of Riemannian <i>F</i>-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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Strachan, Professor Ian and David, Dr Liana
Authors: David, L., and Strachan, I. A.B.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Journal Abbr.:Adv. Math.
ISSN (Online):1090-2082
Published Online:08 December 2010
Copyright Holders:Copyright © 2010 Elsevier Inc.
First Published:First published in Advances in Mathematics 2011 226(5):4031-4060
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
514431Singular structures in Frobenius and tt* geometriesIan StrachanEngineering & Physical Sciences Research Council (EPSRC)EP/H019553/1Mathematics