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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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.
• Publisher: Elsevier
• ISSN: 0001-8708
• 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 Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
51443	1	Singular structures in Frobenius and tt* geometries	Ian Strachan	Engineering & Physical Sciences Research Council (EPSRC)	EP/H019553/1	Mathematics