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Conformal changes of generalized complex structures
TLDR
In this article, the generalized almost complex and almost Hermitian structures that are locally conformal to integrable and to generalized K\"ahler structures, respectively, are characterized.Abstract:
A conformal change of $TM\oplus T^*M$ is a morphism of the form $(X,\alpha)\mapsto(X,e^\tau\alpha)$ $(X\in TM,\alpha\in T^*M,\tau\in C^\infty(M))$ We characterize the generalized almost complex and almost Hermitian structures that are locally conformal to integrable and to generalized K\"ahler structures, respectively, and give examples of such structuresread more
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From Generalized Kähler to Generalized Sasakian Structures
TL;DR: In this article, the authors provide a first introduction to geometric structures on $TM\oplus T^*M. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal, almost) contact and generalized Sasakian structures.
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From generalized Kaehler to generalized Sasakian structures
TL;DR: In this paper, the first introduction to geometric structures on $TM\oplus T^*M$ was provided, which contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal, almost) contact and generalized Sasakian structures.
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Local structure of generalized contact manifolds
TL;DR: In this article, the integrability of a generalized contact pair has been studied and the geometric properties of these structures have been analyzed. But the results were limited to generalized contact pairs and not generalized complex manifolds.
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From locally conformally Kähler to bi-Hermitian structures on non-Kähler complex surfaces
TL;DR: In this paper, it was shown that locally conformally Kahler metrics on certain compact complex surfaces with odd first Betti number can be deformed to new examples of bi-hermitian metrics.
Selected problems and results of topological algebra
TL;DR: In this paper, the notion of totally bounded ness and distinct notions of compactness are studied for topological algebras of a given signature, and the general properties of free topological algebraic topologies and compactifications are investigated.
References
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Riemannian Geometry of Contact and Symplectic Manifolds
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
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Generalized complex geometry
TL;DR: In this paper, the concept of a generalized Kahler manifold has been introduced, which is equivalent to a bi-Hermitian geometry with torsion first discovered by physicists.
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Generalized Calabi-Yau manifolds
TL;DR: A geometrical structure on even-dimensional manifolds is defined in this paper, which generalizes the notion of a Calabi-Yau manifold and also a symplectic manifold.
Book
Lectures on the geometry of Poisson manifolds
TL;DR: In this paper, the Schouten-Nijenhuis bracket is used for quantization of Poisson manifolds, and the bracket of 1-forms is used to quantize Poisson manifold structures.
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Twisted multiplets and new supersymmetric non-linear σ-models☆☆☆★
TL;DR: In this paper, the twisted chiral multiplet is used to formulate supersymmetric nonlinear σ-models with N = 2,4 extended supersymmetry, which fall outside the classification given by Alvarez-Gaume and Freedman.