On Riemannian 4-manifolds and their twistor spaces: a moving frame approach

DOI10.1002/mana.202300577MaRDI QIDQ6656200

Davide Dameno, Giovanni Catino, Paolo Mastrolia

Publication date: 2 January 2025

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

zbMATH Keywords

4-manifoldEinstein manifoldtwistor spacemoving frames

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Twistor methods in differential geometry (53C28) Methods of local Riemannian geometry (53B21)

Cites Work

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• Twistor spaces
• Twistor geometry of Riemannian 4-manifolds by moving frames
• Complex analytic coordinates in almost complex manifolds
• On twistor spaces of the class \({\mathcal C}\)
• Curvature properties of the Chern connection of twistor spaces
• The sixteen classes of almost Hermitian manifolds and their linear invariants
• On the Riemannian curvature of a twistor space
• Hermitian structures on twistor spaces
• Harmonic almost-complex structures on twistor spaces
• Kähler curvature identities for twistor spaces
• Explicit self-dual metrics on \({\mathbb{C}}{\mathbb{P}}_ 2\#\cdots \#{\mathbb{C}}{\mathbb{P}}_ 2\)
• Symplectic Calabi-Yau manifolds, minimal surfaces and the hyperbolic geometry of the conifold
• Einstein manifolds
• Rigidity results for Riemannian twistor spaces under vanishing curvature conditions
• Maximum Principles and Geometric Applications
• Twistor Spaces with Hermitian Ricci Tensor
• On Einstein Metrics on the Twistor Space of a Four‐Dimensional Riemannian Manifold
• Kählerian Twistor Spaces
• Compact four-dimensional self-dual EINSTEIN manifolds with positive scalar curvature
• Self-duality in four-dimensional Riemannian geometry
• Polygons and gravitons
• The Riemannian Goldberg–Sachs Theorem
• A Perspective on Canonical Riemannian Metrics
• Twistor Algebra
• Symplectic twistor spaces
• Nearly Kähler 6-manifolds with reduced holonomy
• Compact four-dimensional Einstein manifolds

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