Any Hermitian metric of constant non-positive (Hermitian) holomorphic sectional curvature on a compact complex surface is Kähler

DOI10.1007/BF01159161zbMath0549.53063MaRDI QIDQ799959

Andrew Balas, Paul Gauduchon

Publication date: 1985

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

Full work available at URL: https://eudml.org/doc/173607

zbMATH Keywords

complex surfaceHermitian metricKähler metricHermitian holomorphic sectional curvature

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55)

Related Items (15)

HERMITIAN METRIC WITH CONSTANT HOLOMORPHIC SECTIONAL CURVATURE ON CONVEX DOMAINS ⋮ Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics ⋮ Almost-Hermitian geometry ⋮ Pluriclosed manifolds with constant holomorphic sectional curvature ⋮ On the Gauduchon curvature of Hermitian manifolds ⋮ Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold ⋮ Curvature properties of twistor spaces ⋮ Compact self-dual Hermitian surfaces ⋮ Closed almost Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler ⋮ Scalar curvature on compact complex manifolds ⋮ Complex nilmanifolds with constant holomorphic sectional curvature ⋮ Holomorphic curvatures of twistor spaces ⋮ Curvature properties of the Chern connection of twistor spaces ⋮ Compact Hermitian surfaces with pointwise constant Gauduchon holomorphic sectional curvature ⋮ On Strominger space forms

Cites Work

• Compact Hermitian manifolds of constant holomorphic sectional curvature
• On Locally and Globally Conformal Kahler Manifolds
• On the Structure of Compact Complex Analytic Surfaces, I
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