Morse-Novikov cohomology of locally conformally Kähler manifolds

DOI10.1016/j.geomphys.2008.11.003zbMath1161.57015arXiv0712.0107OpenAlexW2163370999MaRDI QIDQ1009687

Liviu Ornea, Misha Verbitsky

Publication date: 3 April 2009

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

Full work available at URL: https://arxiv.org/abs/0712.0107

zbMATH Keywords

Bott-Chern cohomologyVaisman manifoldlocally conformal Kähler structureMorse-Novikov cohomologyweight bundle

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Other complex differential geometry (53C56)

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Cites Work

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• Locally conformal Kähler manifolds with potential
• Géométrie des algèbres de Lie locales de Kirillov
• Examples of four-dimensional compact locally conformal Kähler solvmanifolds
• Foliations on Riemannian manifolds
• Les variétés de Poisson et leurs algèbres de Lie associees
• Locally conformally Kähler metrics on Hopf surfaces
• Locally conformal Kähler geometry
• Structure theorem for compact Vaisman manifolds
• On the metric structure of non-Kähler complex surfaces
• An immersion theorem for Vaisman manifolds
• On surfaces of class VII\(_0\)
• On the computation of the Lichnerowicz--Jacobi cohomology.
• Stable bundles on positive principal elliptic fibrations
• Examples of non \(d_{\omega}\)-exact locally conformal symplectic forms
• The pseudo-effective cone of a non-Kählerian surface and applications
• Geometric flow on compact locally conformally Kähler manifolds
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• Note on locally conformal Kähler surfaces