On the Riemannian curvature of a twistor space

DOI10.1007/BF01903962zbMath0747.53030WikidataQ115393058 ScholiaQ115393058MaRDI QIDQ1187329

O. Muskarov, Johann Davidov

Publication date: 28 June 1992

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

zbMATH Keywords

holomorphic sectional curvatureRiemannian submersionsRicci-curvature

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Other complex differential geometry (53C56)

Related Items (19)

Harmonic Hermitian structures on Riemannian manifolds with skew torsion ⋮ \(Sp(n)U(1)\)-connections with parallel totally skew-symmetric torsion ⋮ Twistorial construction of minimal hypersurfaces ⋮ Compatible almost complex structures on twistor spaces and their Gray-Hervella classes ⋮ On a natural map between twistor spaces ⋮ Rigidity results for Riemannian twistor spaces under vanishing curvature conditions ⋮ Curvature properties of twistor spaces ⋮ HOLOMORPHIC AND KILLING VECTOR FIELDS ON COMPACT BALANCED HERMITIAN MANIFOLDS ⋮ Almost complex structures that are harmonic maps ⋮ Harmonicity of the Atiyah-Hitchin-Singer and Eells-Salamon almost complex structures ⋮ Holomorphic curvatures of twistor spaces ⋮ Harmonic and holomorphic 1-forms on compact balanced Hermitian manifolds ⋮ Einstein condition and twistor spaces of compatible partially complex structures ⋮ Partial integrability of compatible almost complex structures on twistor spaces ⋮ Curvature properties of the Chern connection of twistor spaces ⋮ Twistorial examples of Riemannian almost product manifolds and their Gil–Medrano and Naveira types ⋮ Hypersurfaces of the nearly Kähler twistor spaces \(\mathbb{C}\mathrm{P}^3\) and \(\mathbb{F}_{1,2} \) ⋮ Harmonic almost-complex structures on twistor spaces ⋮ Harmonicity of proper almost complex structures on Walker 4-manifolds

Cites Work

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• The fundamental equations of a submersion
• 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

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