Compact Hermitian manifolds of constant holomorphic sectional curvature

DOI10.1007/BF01175044zbMath0575.53044MaRDI QIDQ1064557

Andrew Balas

Publication date: 1985

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

Full work available at URL: https://eudml.org/doc/173576

zbMATH Keywords

holomorphic sectional curvaturecomplex Lie groupG-invariant Hermitian metricnon-Kähler Hermitian manifolds

Mathematics Subject Classification ID

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

Related Items (29)

HERMITIAN METRIC WITH CONSTANT HOLOMORPHIC SECTIONAL CURVATURE ON CONVEX DOMAINS ⋮ On the sum of the Hermitian scalar curvatures of a compact Hermitian manifold ⋮ Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics ⋮ Homogeneous Hermitian manifolds and special metrics ⋮ Locally conformally Hermitian-flat manifolds ⋮ Pluriclosed manifolds with constant holomorphic sectional curvature ⋮ Characterizations of complex Finsler metrics ⋮ Remarks on Chern-Einstein Hermitian metrics ⋮ Second Chern-Einstein metrics on four-dimensional almost-Hermitian manifolds ⋮ Hermitian surfaces of constant holomorphic sectional curvature ⋮ On the Chern-Yamabe flow ⋮ Hermitian metrics of constant Chern scalar curvature on ruled surfaces ⋮ Curvature properties of twistor spaces ⋮ Compact self-dual Hermitian surfaces ⋮ HOLOMORPHIC AND KILLING VECTOR FIELDS ON COMPACT BALANCED HERMITIAN MANIFOLDS ⋮ Closed almost Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler ⋮ Compact Hermitian surfaces of constant antiholomorphic sectional curvatures ⋮ Compact Hermitian surfaces of Einstein type with respect to the Hermitian connection ⋮ Scalar curvature on compact complex manifolds ⋮ Stable type solutions of the complex Laplacian operators on Hermitian manifolds ⋮ Complex nilmanifolds with constant holomorphic sectional curvature ⋮ Holomorphic curvatures of twistor spaces ⋮ Harmonic and holomorphic 1-forms on compact balanced Hermitian manifolds ⋮ On some applications of Gauduchon metrics ⋮ Curvature properties of the Chern connection of twistor spaces ⋮ Hermitian conformal classes and almost Kähler structures on 4-manifolds ⋮ Compact Hermitian surfaces with pointwise constant Gauduchon holomorphic sectional curvature ⋮ Any Hermitian metric of constant non-positive (Hermitian) holomorphic sectional curvature on a compact complex surface is Kähler ⋮ On Strominger space forms

Cites Work

• Tensorfields and curvature in Hermitian manifolds with torsion
• On holomorphic sections of certain hermitian vector bundles
• Fibrés hermitiens à endomorphisme de Ricci non négatif
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