Vanishing theorems on complete Riemannian manifold with a parallel 1‐form

DOI10.1002/mana.202000065zbMath1526.53067arXiv1904.09436OpenAlexW4205506261WikidataQ113914302 ScholiaQ113914302MaRDI QIDQ6094017

Qiang Tan, Teng Huang

Publication date: 9 October 2023

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.09436

zbMATH Keywords

harmonic formsVaisman manifoldsMorse-Novikov cohomology

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) de Rham theory in global analysis (58A12) Hodge theory in global analysis (58A14) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (1)

On harmonic symmetries for locally conformally Kähler manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Manifolds with parallel differential forms and Kähler identities for \(G_{2}\)-manifolds
• \(L^2\) harmonic forms on some complete Kähler manifolds
• \(L^ 2\)-cohomology and index theorem for the Bergman metric
• Locally conformal Kähler manifolds with potential
• Morse-Novikov cohomology of locally conformally Kähler manifolds
• Géométrie des algèbres de Lie locales de Kirillov
• Les variétés de Poisson et leurs algèbres de Lie associees
• \(L_ 2\) cohomology of pseudoconvex domains with complete Kähler metric
• \(L_ 2\) cohomology of the Bergman metric for weakly pseudoconvex domains
• Locally conformal Kähler geometry
• Sheaves in topology
• \(L^2\)-cohomology of hyperkähler quotients
• L//2 cohomology of warped products and arithmetic groups
• On the computation of the Lichnerowicz--Jacobi cohomology.
• Vanishing theorems for \(L^2\)-cohomology on infinite coverings of compact Kähler manifolds and applications in algebraic geometry
• Positivity of LCK potential
• \(L^2\) harmonic forms on complete special holonomy manifolds
• Kähler hyperbolicity and \(L_ 2\)-Hodge theory
• Automorphisms of Locally Conformally Kähler Manifolds
• The Hamiltonian formalism and a many-valued analogue of Morse theory
• On Locally and Globally Conformal Kahler Manifolds
• Kähler parabolicity and the Euler number of compact manifolds of non-positive sectional curvature

This page was built for publication: Vanishing theorems on complete Riemannian manifold with a parallel 1‐form