Generalized Kähler Manifolds, Commuting Complex Structures, and Split Tangent Bundles

Apostolov, Vestislav; Gualtieri, Marco

doi:10.1007/s00220-007-0196-4

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Generalized Kähler Manifolds, Commuting Complex Structures, and Split Tangent Bundles

Author(s): Vestislav Apostolov , Marco Gualtieri

Publication date (Print): February 13 2007

Journal: Communications in Mathematical Physics

Publisher: Springer Nature

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Most cited references 22

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Twisted multiplets and new supersymmetric non-linear σ-models

S.J. Gates, C.M. Hull, M. Roc̆ek (1984)

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On the metric structure of non-Kähler complex surfaces

Florin Alexandru Belgun (2000)

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Instantons, Poisson structures and generalized Kaehler geometry

Nigel Hitchin (2005)

Using the idea of a generalized Kaehler structure, which is a pair of commuting generalized complex structures, we construct bihermitian metrics on the projective plane and the product of two projective lines, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M. We highlight the role of holomorphic Poisson structures in all these constructions.