Geodesic
Systems of symplectic forms on four-manifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 3, pp. 717-734

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We study almost-Hermitian 4-manifolds with holonomy algebra, for the canonical Hermitian connection, of dimension at most one. We show how Riemannian 4-manifolds admitting five orthonormal symplectic forms fit in this picture and we classify them. In this set-up we also fully describe almost-Kähler 4-manifolds.

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Classification : 74K20, 74B20 
@article{ASNSP_2013_5_12_3_717_0,
     author = {Chiossi, Simon G. and Nagy, Paul-Andi},
     title = {Systems of symplectic forms on four-manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {717--734},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {3},
     year = {2013},
     mrnumber = {3137461},
     zbl = {1295.53083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_3_717_0/}
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Chiossi, Simon G.; Nagy, Paul-Andi. Systems of symplectic forms on four-manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 3, pp. 717-734. http://geodesic.mathdoc.fr/item/ASNSP_2013_5_12_3_717_0/