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Hypersymplectic structures on Courant algebroids
1. | CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal, Portugal |
References:
[1] |
P. Antunes, Crochets de Poisson Gradués et Applications: Structures Compatibles et Généralisations des Structures Hyperkählériennes,, Ph.D thesis, (2010). Google Scholar |
[2] |
P. Antunes, C. Laurent-Gengoux and J. M. Nunes da Costa, Hierarchies and compatibility on Courant algebroids,, Pac. J. Math., 261 (2013), 1.
doi: 10.2140/pjm.2013.261.1. |
[3] |
P. Antunes and J. M. Nunes da Costa, Hyperstructures on Lie algebroids,, Rev. in Math. Phys., 25 (2013).
doi: 10.1142/S0129055X13430034. |
[4] |
P. Antunes and J. M. Nunes da Costa, Induced hypersymplectic and hyperkähler structures on the dual of a Lie algebroid,, Int. J. Geom. Meth. Mod. Phys., 11 (2014).
doi: 10.1142/S0219887814600305. |
[5] |
P. Antunes and J. M. Nunes da Costa, Hyperstructures with torsion on Lie algebroids, preprint,, , (). Google Scholar |
[6] |
H. Bursztyn, G. Cavalcanti and M. Gualtieri, Generalized Kähler and hyper-Kähler quotients,, in Poisson geometry in mathematics and physics, 450 (2008), 61.
doi: 10.1090/conm/450/08734. |
[7] |
P. S. Howe and G. Papadopoulos, Twistor spaces for hyper-Kähler manifolds with torsion,, Phys. Lett. B, 379 (1996), 80.
doi: 10.1016/0370-2693(96)00393-0. |
[8] |
J. Grabowski, Courant-Nijenhuis tensors and generalized geometries,, in Groups, 29 (2006), 101.
|
[9] |
N. Hitchin, Generalized Calabi-Yau manifolds,, Q. J. Math., 54 (2003), 281.
doi: 10.1093/qmath/hag025. |
[10] |
Y. Kosmann-Schwarzbach, Quasi, twisted, and all that ... in Poisson geometry and Lie algebroid theory,, in The Breadth of symplectic and Poisson geometry, (2005), 363.
doi: 10.1007/0-8176-4419-9_12. |
[11] |
Y. Kosmann-Schwarzbach, Poisson and symplectic functions in Lie algebroid theory,, in Higher Structures in Geometry and Physics, (2011), 243.
doi: 10.1007/978-0-8176-4735-3_12. |
[12] |
D. Roytenberg, On the structure of graded symplectic supermanifolds and Courant algebroids,, in Quantization, (2002), 169.
doi: 10.1090/conm/315/05479. |
[13] |
D. Roytenberg, Quasi-Lie bialgebroids and twisted Poisson manifolds,, Lett. Math. Phys., 61 (2002), 123.
doi: 10.1023/A:1020708131005. |
[14] |
M. Stiénon, Hypercomplex structures on Courant algebroids,, C. R. Acad. Sci. Paris, 347 (2009), 545.
doi: 10.1016/j.crma.2009.02.020. |
[15] |
T. Voronov, Graded manifolds and Drinfeld doubles for Lie bialgebroids,, in Quantization, (2002), 131.
doi: 10.1090/conm/315/05478. |
[16] |
P. Xu, Hyper-Lie Poisson structures,, Ann. Sci. École Norm. Sup., 30 (1997), 279.
doi: 10.1016/S0012-9593(97)89921-1. |
show all references
References:
[1] |
P. Antunes, Crochets de Poisson Gradués et Applications: Structures Compatibles et Généralisations des Structures Hyperkählériennes,, Ph.D thesis, (2010). Google Scholar |
[2] |
P. Antunes, C. Laurent-Gengoux and J. M. Nunes da Costa, Hierarchies and compatibility on Courant algebroids,, Pac. J. Math., 261 (2013), 1.
doi: 10.2140/pjm.2013.261.1. |
[3] |
P. Antunes and J. M. Nunes da Costa, Hyperstructures on Lie algebroids,, Rev. in Math. Phys., 25 (2013).
doi: 10.1142/S0129055X13430034. |
[4] |
P. Antunes and J. M. Nunes da Costa, Induced hypersymplectic and hyperkähler structures on the dual of a Lie algebroid,, Int. J. Geom. Meth. Mod. Phys., 11 (2014).
doi: 10.1142/S0219887814600305. |
[5] |
P. Antunes and J. M. Nunes da Costa, Hyperstructures with torsion on Lie algebroids, preprint,, , (). Google Scholar |
[6] |
H. Bursztyn, G. Cavalcanti and M. Gualtieri, Generalized Kähler and hyper-Kähler quotients,, in Poisson geometry in mathematics and physics, 450 (2008), 61.
doi: 10.1090/conm/450/08734. |
[7] |
P. S. Howe and G. Papadopoulos, Twistor spaces for hyper-Kähler manifolds with torsion,, Phys. Lett. B, 379 (1996), 80.
doi: 10.1016/0370-2693(96)00393-0. |
[8] |
J. Grabowski, Courant-Nijenhuis tensors and generalized geometries,, in Groups, 29 (2006), 101.
|
[9] |
N. Hitchin, Generalized Calabi-Yau manifolds,, Q. J. Math., 54 (2003), 281.
doi: 10.1093/qmath/hag025. |
[10] |
Y. Kosmann-Schwarzbach, Quasi, twisted, and all that ... in Poisson geometry and Lie algebroid theory,, in The Breadth of symplectic and Poisson geometry, (2005), 363.
doi: 10.1007/0-8176-4419-9_12. |
[11] |
Y. Kosmann-Schwarzbach, Poisson and symplectic functions in Lie algebroid theory,, in Higher Structures in Geometry and Physics, (2011), 243.
doi: 10.1007/978-0-8176-4735-3_12. |
[12] |
D. Roytenberg, On the structure of graded symplectic supermanifolds and Courant algebroids,, in Quantization, (2002), 169.
doi: 10.1090/conm/315/05479. |
[13] |
D. Roytenberg, Quasi-Lie bialgebroids and twisted Poisson manifolds,, Lett. Math. Phys., 61 (2002), 123.
doi: 10.1023/A:1020708131005. |
[14] |
M. Stiénon, Hypercomplex structures on Courant algebroids,, C. R. Acad. Sci. Paris, 347 (2009), 545.
doi: 10.1016/j.crma.2009.02.020. |
[15] |
T. Voronov, Graded manifolds and Drinfeld doubles for Lie bialgebroids,, in Quantization, (2002), 131.
doi: 10.1090/conm/315/05478. |
[16] |
P. Xu, Hyper-Lie Poisson structures,, Ann. Sci. École Norm. Sup., 30 (1997), 279.
doi: 10.1016/S0012-9593(97)89921-1. |
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