Generalized Kähler manifolds, commuting complex structures, and split tangent bundles

DOI10.1007/s00220-007-0196-4zbMath1135.53018arXivmath/0605342OpenAlexW1999318515MaRDI QIDQ2472454

Marco Gualtieri, Vestislav Apostolov

Publication date: 22 February 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605342

zbMATH Keywords

positive curvaturegeneralized Kähler structure

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (39)

A note on submanifolds and mappings in generalized complex geometry ⋮ Pluriclosed flow on generalized Kähler manifolds with split tangent bundle ⋮ Formality in generalized Kähler geometry ⋮ Hermitian structures on a class of almost nilpotent solvmanifolds ⋮ The Hitchin-Kobayashi correspondence for quiver bundles over generalized Kähler manifolds ⋮ Odd type generalized complex structures on 4-manifolds ⋮ Two-step solvable SKT shears ⋮ Bi-Hermitian metrics on Kato surfaces ⋮ Generalized Kähler geometry ⋮ Complex surfaces and null conformal Killing vector fields ⋮ Generalized coKähler geometry and an application to generalized Kähler structures ⋮ Variational structure and uniqueness of generalized Kähler-Ricci solitons ⋮ Global viscosity solutions of generalized Kähler-Ricci flow ⋮ On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics ⋮ The minimal model for the Batalin-Vilkovisky operad ⋮ Blowing up generalized Kähler 4-manifolds ⋮ Non-Kähler Calabi-Yau geometry and pluriclosed flow ⋮ Superconformal structures on generalized Calabi-Yau metric manifolds ⋮ Generalized almost para-contact manifolds ⋮ Deformation classes in generalized Kähler geometry ⋮ On a question of Vaisman concerning complex surfaces ⋮ Pluriclosed Flow and the Geometrization of Complex Surfaces ⋮ On generalized Gauduchon metrics ⋮ Classical and quantum aspects of Yang-Baxter Wess-Zumino models ⋮ Generalized pseudo-Kähler structures ⋮ On holomorphic maps and generalized complex geometry ⋮ Generalized Kähler-Ricci flow and the classification of nondegenerate generalized Kähler surfaces ⋮ Generalized Moser lemma ⋮ Special Hermitian metrics and Lie groups ⋮ Generalized Kähler almost abelian Lie groups ⋮ Poisson sigma model on the sphere ⋮ The equivariant cohomology theory of twisted generalized complex manifolds ⋮ Pluriclosed flow, Born-Infeld geometry, and rigidity results for generalized Kähler manifolds ⋮ Generalized para-Kähler manifolds ⋮ Lectures on generalized complex geometry for physicists ⋮ Blow-ups and resolutions of strong Kähler with torsion metrics ⋮ Special Hermitian metrics on compact solvmanifolds ⋮ The pluriclosed flow on nilmanifolds and tamed symplectic forms ⋮ The Gibbons-Hawking ansatz in generalized Kähler geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized complex geometry
• Every K 3 surface is Kähler
• Instantons, Poisson structures and generalized Kähler geometry
• On solvable generalized Calabi-Yau manifolds
• Reduction of Courant algebroids and generalized complex structures
• Symmetries in generalized Kähler geometry
• Generalized Kähler manifolds and off-shell supersymmetry
• Some curvature properties of complex surfaces
• Geometric structures on compact complex analytic surfaces
• Applications of the Kaehler-Einstein-Calabi-Yau metric to moduli of K3 surfaces
• Courants kählériens et surfaces compactes. (Kähler currents and compact surfaces)
• On compact Kähler surfaces
• Explicit doubly-Hermitian metrics
• Complex structures on Riemannian four-manifolds
• On the metric structure of non-Kähler complex surfaces
• Properties of manifolds with skew-symmetric torsion and special holonomy
• On surfaces of class VII\(_0\)
• Poisson geometry of sigma models with extended supersymmetry
• Bihermitian Structures on Complex Surfaces
• CLASSIFICATION OF POISSON SURFACES
• Generalized Calabi-Yau Manifolds
• On surfaces of class VII with numerically anticanonical divisor
• Special metrics on compact complex manifolds
• Bihermitian surfaces with odd first Betti number

This page was built for publication: Generalized Kähler manifolds, commuting complex structures, and split tangent bundles