This is a generalization of the procedure presented in [3] to construct semisimple bi-flat F-manifolds (M, (1)(2),o,*,e,E) starting from homogeneous solutions of degree -1 of the Darboux-Egorov system. The Lamé coefficients Hi involved in the construction are still homogeneous functions of a certain degree di but we consider the general case di≠dj. As a consequence the rotation coefficients βij are homogeneous functions of degree d i-dj-1. It turns out that any semisimple bi-flat F-manifold satisfying a natural additional assumption can be obtained in this way. Finally, building on the well-known relation between the three-wave system and Painlevé VI, we show that three-dimensional, semisimple, bi-flat F-manifolds can be constructed starting from generic solutions of Painlevé VI. © 2013 The Author(s) 2013. Published by Oxford University Press. All rights reserved.

Lorenzoni, P. (2014). Darboux–Egorov System, Bi-flat F-Manifolds and Painlevé VI. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014(12), 3279-3302 [10.1093/imrn/rnt045].

Darboux–Egorov System, Bi-flat F-Manifolds and Painlevé VI

Lorenzoni, P
2014

Abstract

This is a generalization of the procedure presented in [3] to construct semisimple bi-flat F-manifolds (M, (1)(2),o,*,e,E) starting from homogeneous solutions of degree -1 of the Darboux-Egorov system. The Lamé coefficients Hi involved in the construction are still homogeneous functions of a certain degree di but we consider the general case di≠dj. As a consequence the rotation coefficients βij are homogeneous functions of degree d i-dj-1. It turns out that any semisimple bi-flat F-manifold satisfying a natural additional assumption can be obtained in this way. Finally, building on the well-known relation between the three-wave system and Painlevé VI, we show that three-dimensional, semisimple, bi-flat F-manifolds can be constructed starting from generic solutions of Painlevé VI. © 2013 The Author(s) 2013. Published by Oxford University Press. All rights reserved.
Articolo in rivista - Articolo scientifico
F-Manifolds, Painlevé equations,
English
2014
2014
12
3279
3302
none
Lorenzoni, P. (2014). Darboux–Egorov System, Bi-flat F-Manifolds and Painlevé VI. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014(12), 3279-3302 [10.1093/imrn/rnt045].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/44691
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