Generalized Calabi-Yau manifolds

Abstract

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 type and can be transformed by the action of both diffeomorphisms and closed 2-forms. In the special case of six dimensions we characterize them as critical points of a natural variational problem on closed forms, and prove that a local moduli space is provided by an open set in either the odd or even cohomology.

37 pages, LateX

Cited by in corpus (59)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• Gauged Supergravities
• 6D microstate geometries from 10D structures
• New supersymmetric AdS4 type II vacua
• On moduli and effective theory of N=1 warped flux compactifications
• Brane Effective Actions, Kappa-Symmetry and Applications
• E7(7) formulation of N=2 backgrounds
• Poisson-Lie U-duality in Exceptional Field Theory
• N=2 solutions of massive type IIA and their Chern-Simons duals
• Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models
• Emergent Spacetime and The Origin of Gravity
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• D-branes and doubled geometry
• Flux backgrounds from Twists
• The rotation curve of a point particle in stringy gravity
• Domain walls from ten dimensions
• Stable generalized complex structures
• Heterotic compactifications on SU(2)-structure backgrounds
• Courant Algebroids. A Short History
• Type II compactifications on manifolds with SU(2) x SU(2) structure
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• $\mathbf{O}(D,D)$ completion of the Friedmann equations
• Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry
• Gravity theory on Poisson manifold with $R$-flux
• Generalising G${}_{\text{2}}$ geometry: involutivity, moment maps and moduli
• Multiplicative Dirac structures
• T-duality, Non-geometry and Lie Algebroids in Heterotic Double Field Theory
• Semichiral Fields on S^2 and Generalized Kähler Geometry
• Topological Strings on Non-Commutative Resolutions
• Cartan Connections on Lie Groupoids and their Integrability
• Patterns in Calabi-Yau Distributions
• AdS Vacua, Attractor Mechanism and Generalized Geometries
• An N=2 worldsheet approach to D-branes in bihermitian geometries: II. The general case
• Type one generalized Calabi--Yaus
• (2,2) Geometry from Gauge Theory
• Supergravity without gravity and its BV formulation
• A Hodge-Type Decomposition of Holomorphic Poisson Cohomology on Nilmanifolds
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• A Curvature Flow Unifying Symplectic Curvature Flow And Pluriclosed Flow
• Dynamical phase space from a SO(d,d) matrix model
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• Perturbations in $\mathbf{O}(D,D)$ string cosmology from double field theory
• Generalized almost paracontact structures
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Integrable sigma models with complex and generalized complex structures
• Open-String Non-Associativity in an R-flux Background
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• Singular Reduction of Generalized Complex Manifolds
• Topological field theories of 2- and 3-forms in six dimensions
• Pin(d,d) covariance of pure spinor equations for supersymmetric vacua and Non-Abelian T-duality
• Differential calculus for generalized geometry and geometric Lax flows
• On canonical metrics of complex surfaces with split tangent and related geometric PDEs
• Towards a T-dual Emergent Gravity
• T-duality on Almost Hermitian Spaces
• A T-Fold Black Hole in Doubled Type IIB
• Instances of Higher Geometry in Field Theory
• Optimal Transport and Generalized Ricci Flow