Levi-Civita Ricci-flat metrics on non-Kähler Calabi-Yau manifolds

DOI10.1007/s12220-022-01114-8OpenAlexW4313888325MaRDI QIDQ2679626

Eder M. Correa

Publication date: 23 January 2023

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.04824

zbMATH Keywords

curvaturesChern-Ricci flowHermitian manifoldslocally conformal Kähler manifoldsHermitian-Weyl manifoldsWeyl-Einstein manifolds

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Local differential geometry of Hermitian and Kählerian structures (53B35) Conformal structures on manifolds (53C18) Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) (53E30)

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Cites Work

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• Cohomological aspects in complex non-Kähler geometry
• Convergence of the parabolic complex Monge-Ampère equation on compact Hermitian manifolds
• An equivalence of scalar curvatures on Hermitian manifolds
• Sasaki-Einstein 5-manifolds associated to toric 3-Sasaki manifolds
• On manifolds homeomorphic to the 7-sphere
• Einstein metrics on spheres
• Obstructions to the existence of Sasaki-Einstein metrics
• La 1-forme de torsion d'une variété hermitienne compacte
• The sixteen classes of almost Hermitian manifolds and their linear invariants
• Deformations of Sasakian structures and its application to the Brieskorn manifolds
• On a generalization of the Hopf fibration. I
• Einstein-Hermitian surfaces and Hermitian Einstein-Weyl structures in dimension 4
• Locally conformal Kähler geometry
• New Einstein metrics in dimension five.
• On locally conformal symplectic manifolds of the first kind
• Minimal complex surfaces with Levi-Civita Ricci-flat metrics
• Generalized Hopf manifolds
• On the evolution of a Hermitian metric by its Chern-Ricci form
• Levi-Civita Ricci-flat metrics on compact complex manifolds
• Beispiele zur Differentialtopologie von Singularitäten
• Some complex structures on products of homotopy spheres
• Groups of homotopy spheres. I
• The Chern–Ricci flow on complex surfaces
• Sasaki-Einstein Manifolds
• The behavior of the Chern scalar curvature under the Chern-Ricci flow
• Ricci curvatures on Hermitian manifolds
• Differential Analysis on Complex Manifolds
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Locally conformal Kähler reduction
• Structures de Weyl-Einstein, espace de twisteurs et variétés de type S1 x S3.
• EXAMPLES OF SINGULAR NORMAL COMPLEX SPACES WHICH ARE TOPOLOGICAL MANIFOLDS
• Formules de Picard-Lefschetz généralisées et ramification des intégrales