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We characterize the Dirac structures that are parallel with respect to Gualtieri's canonical connection of a generalized Riemannian metric.
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M. Gualtieri, Generalized complex geometry, Ph.D. thesis, Univ. Oxford, 2003; arXiv:math.DG/0401221
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N. J. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math., 54 (2003), 281-308
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I. Vaisman, Isotropic Subbundles of T M ⊕ T ∗ M TM\oplus T^{*}M , Intern. J. of Geom. Methods in Modern Physics, 4(3) (2007),487-516
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I. Vaisman, Generalized CRF-structures, Geometriae Dedicata, 133 (2008),129-154
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M. Gualtieri, Branes of Poisson variety, in : The many Facets of Geometry. A tribute to Nigel Hitchin (O. Garcia-Prado, J. P. Bourguignon and S. salamon, eds.), Oxford Univ. Press, Oxford, 2010, 368-395
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I. Vaisman, From Generalized Kähler to Generalized Sasakian Strucutres, J. of Geom. and Symmetry in Physics, 18 (2010), 63-86
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2006
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I. T. Ellwood, NS-NS fluxes in Hitchin’s generalized geometry, arXiv:hep-th/0612100v4
Cited in the paper.
Y. S. Poon and A. wade, Generalized contact structures, J. London Math. Soc., 83 (2011), 309-332
2011
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