Hamiltonian Symmetries and Reduction in Generalized Geometry
By Shengda Hu. 2005
51 citations recorded by the source corpus.
A closed 3-form H ∈ Ω0(M) defines an extension of Γ(TM) by Ω0(M). This fact leads to the definition of the group of H-twisted Hamiltonian symmetries Ham(M, J;H) as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold. The Hamiltonian reduction in the category of generalized complex geometry is then constructed. The definitions and constructions are natural extensions of the corresponding ones in the symplectic geometry. We describe cutting in generalized complex geometry to show that it’s a general phenomenon in generalized geometry that topology change is often accompanied by twisting (class) change.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6a5f60373f0d12e54bc8a07beecd1588b13836d0
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Reduction and submanifolds of generalized complex manifolds (2005, background): “nection in his lecture at the conference in Trieste, Italy, July 2005. 2 While work on this paper was in progress, several papers on reduction of generalized complex structures were posted on the web [12, 14, 22, 3, 15]. These papers provide various ways of extending the notion of a Hamiltonian Lie ”