Systems of symplectic forms on four-manifolds

Chiossi, Simon G.; Nagy, Paul-Andi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 3, pp. 717-734.

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.

Classification : 74K20, 74B20

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