Abstract
In this paper we present a construction of Ricci-flat connections through an induction procedure. Given a symplectic manifold (M, ω) of dimension 2n, we define induction as a way to construct a symplectic manifold (P, μ) of dimension 2n + 2. Given any symplectic manifold (M, ω) of dimension 2n and given a symplectic connection ▽ on (M, ω), we define induction as a way to construct a symplectic manifold (P, μ) of dimension 2n+2 and an induced connection ▽P which is a Ricci-flat symplectic connection on (P, μ).
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References
Michel Cahen, Simone Gutt, Lorenz Schwachhöfer: Construction of Ricci-type connections by reduction and induction, preprint math.DG/0310375, in The Breadth of Symplectic and Poisson Geometry, Marsden, J.E. and Ratiu, T.S. (eds), Progress in Math 232, Birkhäuser, 2004, 41–57.
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We are pleased to dedicate this paper to Hideki Omori on the occasion of his 65th birthday
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© 2007 Birkhäuser Boston
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Cahen, M., Gutt, S. (2007). Reduction, Induction and Ricci Flat Symplectic Connections. In: Maeda, Y., Ochiai, T., Michor, P., Yoshioka, A. (eds) From Geometry to Quantum Mechanics. Progress in Mathematics, vol 252. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4530-4_8
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DOI: https://doi.org/10.1007/978-0-8176-4530-4_8
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4512-0
Online ISBN: 978-0-8176-4530-4
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