A simple construction of generalized complex manifolds
classification
🧮 math.DG
keywords
complexgeneralizedmanifoldsnaturalbundlechernconnectionconstruct
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We construct a natural generalized complex structure on the total space of any bundle endowed with a Chern connection and whose typical fibre is a homogeneous symplectic manifold. This extends known constructions of generalized complex structures on Lie groups and leads to natural examples of holomorphic maps between generalized complex manifolds.
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