Reduction of Vaisman structures in complex and quaternionic geometry

DOI10.1016/j.geomphys.2006.01.005zbMath1109.53070arXivmath/0502572OpenAlexW2099822215MaRDI QIDQ857405

Rosa Gini, Maurizio Parton, Paolo Piccinni, Liviu Ornea

Publication date: 14 December 2006

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0502572

zbMATH Keywords

Sasakian manifoldsymplectic reductionLee formHopf manifoldVaisman manifoldHamiltonian actionHKT manifoldlocally conformal Kähler manifoldhypercomplex manifold3-Sasakian manifold

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Momentum maps; symplectic reduction (53D20)

Related Items

LCK rank of locally conformally Kähler manifolds with potential, Toric Vaisman manifolds, \(\mathrm{Spin}(9)\) geometry of the octonionic Hopf fibration, Locally conformally Hessian and statistical manifolds, Locally conformally Kähler solvmanifolds: a survey, Cohomologies of locally conformally symplectic manifolds and solvmanifolds, Locally conformally Kähler structures on unimodular Lie groups, Hermitian ranks of compact complex manifolds, Holomorphic submersions of locally conformally Kähler manifolds, Examples of non-trivial rank in locally conformal Kähler geometry, Locally conformally symplectic and Kähler geometry, Locally conformally symplectic convexity, LCK metrics on toric LCS manifolds

Cites Work

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• The hypercomplex quotient and the quaternionic quotient
• Locally conformal parallel \(G_2\) and \(\operatorname{Spin}(7)\) manifolds
• Hyperkähler metrics and supersymmetry
• Locally conformally Kähler metrics on Hopf surfaces
• The Einstein-Weyl equations in complex and quaternionic geometry
• Hyperkähler manifolds with torsion obtained from hyperholomorphic bundles
• Structure theorem for compact Vaisman manifolds
• On the metric structure of non-Kähler complex surfaces
• Generalized Hopf manifolds
• On surfaces of class VII\(_0\)
• Almost Hermitian structures and quaternionic geometries
• Geometric flow on compact locally conformally Kähler manifolds
• Inhomogeneous hypercomplex structures on homogeneous manifolds
• Potential 1-forms for hyper-K hler structures with torsion
• Locally conformal Kähler reduction
• Reduction of HKT-structures
• Structures de Weyl-Einstein, espace de twisteurs et variétés de type S1 x S3.
• On the Structure of Compact Complex Analytic Surfaces, I
• On the Structure of Compact Complex Analytic Surfaces, II
• On the Structure of Complex Analytic Surfaces, IV
• Locally conformal Kähler structures in quaternionic geometry