Generalized complex geometry

Details Generalized complex geometry Generalized complex geometry

2007-03-11

arxiv.org/abs/math/0703298v2

Mathematics

Differential Geometry

49 pages, refined from math.DG/0401221 and updated with new constructions, added references.

Scientific paper

Generalized complex geometry, introduced by Hitchin, encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and study generalized complex branes, which interpolate between flat bundles on Lagrangian submanifolds and holomorphic bundles on complex submanifolds.

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