Corpus ID: 235358798

Polynomial Structures in Generalized Geometry

@inproceedings{Aldi2021PolynomialSI,
  title={Polynomial Structures in Generalized Geometry},
  author={Marco Aldi and D. Grandini},
  year={2021}
}
On the generalized tangent bundle of a smooth manifold, we study skewsymmetric endomorphisms satisfying an arbitrary polynomial equation with real constant coefficients. We investigate the compatibility of these structures with the de Rham operator and the Courant-Dorfman bracket. In particular, we isolate several conditions that when restricted to the motivating example of generalized almost complex structure are equivalent to the notion of integrability. 

References

SHOWING 1-10 OF 35 REFERENCES
Generalized contact geometry and T-duality
Abstract We study generalized almost contact structures on odd-dimensional manifolds. We introduce a notion of integrability and show that the class of these structures is closed under symmetries ofExpand
Generalized complex geometry
Generalized complex geometry encompasses complex and symplectic ge- ometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group,Expand
Generalized almost product structures and generalized CRF-structures
Abstract We give several equivalent characterizations of orthogonal subbundles of the generalized tangent bundle defined, up to B -field transform, by almost product and local product structures. WeExpand
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
A class of almost tangent structures in generalized geometry
A generalized almost tangent structure on the big tangent bundle T big M associated to an almost tangent structure on M is con- sidered and several features of it are studied with a special viewExpand
An Abstract Morimoto Theorem for Generalized $F$-structures
We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized $F$-structures on manifolds that are not necessarily global products. As applications weExpand
The decomposition of forms and cohomology of generalized complex manifolds
Abstract We study the decomposition of forms induced by a generalized complex structure giving a complete description of the bundles involved and, around regular points, of the operators ∂ and ∂ ¯Expand
Generalized metallic structures
We study the properties of a generalized metallic, a generalized product and a generalized complex structure induced on the generalized tangent bundle of $M$ by a metallic Riemannian structureExpand
Conjugacy classes in linear groups
Abstract Let G belong to one of the three families of complex classical linear groups or to one of the seven families of corresponding real forms. Let L denote its Lie algebra. We give a simple andExpand
Haantjes algebras and diagonalization
Abstract We introduce the notion of Haantjes algebra: It consists of an assignment of a family of operator fields on a differentiable manifold, each of them with vanishing Haantjes torsion. They areExpand
...
1
2
3
4
...