Reduction and submanifolds of generalized complex manifolds
By Izu Vaisman. 2005
91 citations recorded by the source corpus.
Abstract We recall the presentation of the generalized, complex structures by classical tensor fields, while noticing that one has a similar presentation and the same integrability conditions for generalized, paracomplex and subtangent structures. This presentation shows that the generalized, complex, paracomplex and subtangent structures belong to the realm of Poisson geometry. Then, we prove geometric reduction theorems of Marsden–Ratiu and Marsden–Weinstein type for the mentioned generalized structures and give the characterization of the submanifolds that inherit an induced structure via the corresponding classical tensor fields.
Subfields: Astronomy and Astrophysics, Mathematical Physics, Pathology and Forensic Medicine
View Paper: https://www.semanticscholar.org/paper/e0f1aa461debcbf998c5969289e197855e11bdcf
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In Astronomy and Astrophysics
In Mathematical Physics
In Pathology and Forensic Medicine
Citations in the corpus
- Hamiltonian Symmetries and Reduction in Generalized Geometry (2005, background): “Another point of view is provided by [56], which discusses three related stuctures on TM .”
- Homogeneous para-Kähler Einstein manifolds (2009, background): “Replacing the tangent bundle TM in the definition of a para-complex structure by the generalized tangent bundle T (M) and the Nijenhuis bracket by the Courant bracket, Wade [17] andVaisman [18] define the notion of a generalized para-complex structure which unifies the notion of symplectic structure”