Corpus ID: 117593538

New aspects of the ddc-lemma

@article{Cavalcanti2005NewAO,
  title={New aspects of the ddc-lemma},
  author={Gil R. Cavalcanti},
  journal={arXiv: Differential Geometry},
  year={2005}
}
  • G. Cavalcanti
  • Published 2005
  • Mathematics
  • arXiv: Differential Geometry
We produce examples of generalized complex structures on manifolds by generalizing results from symplectic and complex geometry. We produce generalized complex structures on symplectic fibrations over a generalized complex base. We study in some detail different invariant generalized complex structures on compact Lie groups and provide a thorough description of invariant structures on nilmanifolds, achieving a classification on 6-nilmanifolds. We study implications of the `dd^c-lemma' in the… Expand
Cohomology and Hodge Theory on Symplectic Manifolds: III
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies areExpand
Symplectic Foliations and Generalized Complex Structures
  • M. Bailey
  • Mathematics
  • Canadian Journal of Mathematics
  • 2014
Abstract We answer the natural question: when is a transversely holomorphic symplectic foliation induced by a generalized complex structure? The leafwise symplectic form and transverse complexExpand
GENERALIZED MOSER LEMMA
We show how the classical Moser lemma from symplectic geometry extends to generalized complex structures (GCS) on arbitrary Courant algebroids. For this, we extend the notion of a Lie derivative toExpand
Hodge theory and deformations of SKT manifolds
We use tools from generalized complex geometry to develop the theory of SKT (a.k.a. pluriclosed Hermitian) manifolds and more generally manifolds with special holonomy with respect to a metricExpand
Variation of Hodge structure for generalized complex manifolds
Abstract A generalized complex manifold which satisfies the ∂ ∂ ¯ -lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of theExpand
Deformations of generalized complex and generalized Kahler structures
In this paper we obtain a stability theorem of generalized Kahler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stabilityExpand
Bott–Chern cohomology of solvmanifolds
We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott–Chern cohomology. We are especially aimed at studying the Bott–Chern cohomology of specialExpand
Cohomological Aspects on Complex and Symplectic Manifolds
We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomologyExpand
Symplectic cohomologies and deformations
In this note we study the behavior of symplectic cohomology groups under symplectic deformations. Moreover, we show that for compact almost-Kähler manifolds $$(X,J,g,\omega )$$(X,J,g,ω) withExpand
Hamiltonian Symmetries and Reduction in Generalized Geometry
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 LieExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 76 REFERENCES
Generalized Calabi-Yau manifolds
A geometrical structure on even-dimensional manifolds is defined which generalizes the notion of a Calabi–Yau manifold and also a symplectic manifold. Such structures are of either odd or even typeExpand
Mirror symmetry and generalized complex manifolds: Part I. The transform on vector bundles, spinors, and branes
Abstract In this paper we begin the development of a relative version of T -duality in generalized complex geometry which we propose as a manifestation of mirror symmetry. Let M be an n -dimensionalExpand
Some simple examples of symplectic manifolds
This is a construction of closed symplectic manifolds with no Kaehler structure. A symplectic manifold is a manifold of dimension 2k with a closed 2-form a such that ak is nonsingular. If M2k is aExpand
Differential analysis on complex manifolds
* Presents a concise introduction to the basics of analysis and geometry on compact complex manifolds * Provides tools which are the building blocks of many mathematical developments over the pastExpand
Supersymmetric backgrounds from generalized Calabi-Yau manifolds
We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form eiJ andExpand
Formality of canonical symplectic complexes and Frobenius manifolds
It is shown that the de Rham complex of a symplectic manifold $M$ satisfying the hard Lefschetz condition is formal. Moreover, it is shown that the differential Gerstenhaber-Batalin-VilkoviskiExpand
The Mukai pairing, I: the Hochschild structure
We study the Hochschild structure of a smooth space or orbifold, emphasizing the importance of a pairing defined on Hochschild homology which generalizes a similar pairing introduced by Mukai on theExpand
Compact Manifolds with Special Holonomy
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existenceExpand
Topology and H-flux of T-dual manifolds.
TLDR
A general formula for the topology and H-flux of the T-dual of a type II compactification is presented, finding that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of theDual H- flux over the dual circle. Expand
Special metric structures and closed forms
In recent work, N. Hitchin described special geometries in terms of a variational problem for closed generic $p$-forms. In particular, he introduced on 8-manifolds the notion of an integrableExpand
...
1
2
3
4
5
...