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Reduction of Courant algebroids and generalized complex structures
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abstract
We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized K\"ahler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction. The enhanced symmetry group of a Courant algebroid leads us to define \emph{extended} actions and a generalized notion of moment map. Key examples of generalized K\"ahler reduced spaces include new explicit bi-Hermitian metrics on $\CC P^2$.
Forward citations
Cited by 3 Pith papers
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Generalised Complex and Spinor Relations
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
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Gauged Courant sigma models
Gauged Courant sigma models extend Courant sigma models by adding gauge symmetries from Lie algebroids and Courant algebroids, with consistency ensured by flatness conditions on target-space curvatures and torsions.
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Courant Algebroid Relations, T-Dualities and Generalised Ricci Flow
Using Courant algebroid relations, the authors prove that geometric T-duality maps solutions of generalized Ricci flow to solutions of generalized Ricci flow, preserving the generalized string background equations.
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