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In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-K\"ahler manifolds.
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O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, J. High Energy Phys., 1008 (2010), 008
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J. P. Ortega and T. S. Ratiu, Momentum maps and Hamiltonian reduction, Progress in Math., vol 222, Birkhäuser, Boston, 2004
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F. Etayo, R. Santamaría and U. R. Trías, The geometry of a bi-Lagrangian manifold, Diff. Geom. Appl., 24 (2006), 33-59
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F. Fassò and N. Sansonetto, Integrable almost-symplectic Hamiltonian systems, J. Math. Phys. 48, 092902 (2007)
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2012
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I. Vaisman, On the Geometry of Double Field Theory, J. Math. Physics, 53 (2012), 033509
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O. Hohm and B. Zwiebach, Towards an invariant geometry of double field theory, J. Math. Phys. 54, 032303 (2013); http://dx.doi.org/10.1063/1.4795513
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I. Vaisman, Hamiltonian vector fields on almost symplectic manifolds, J. Math. Phys. 54, 092902 (2013);doi: 10.1063/1.4820397
2013
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