On compact Hermitian manifolds with flat Gauduchon connections

DOI10.1007/s10114-018-7409-yzbMath1401.53065arXiv1709.02530OpenAlexW2964336295MaRDI QIDQ1782059

Bo Yang, Fang Yang Zheng

Publication date: 18 September 2018

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02530

zbMATH Keywords

Kähler manifoldsflat connectionHermitian manifoldsHermitian connectionsGauduchon connection

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Local differential geometry of Hermitian and Kählerian structures (53B35) Linear and affine connections (53B05)

Related Items (15)

On Strominger Kähler-like manifolds with degenerate torsion ⋮ Pluriclosed manifolds with constant holomorphic sectional curvature ⋮ Hermitian geometry of Lie algebras with abelian ideals of codimension 2 ⋮ Strominger connection and pluriclosed metrics ⋮ Affine Connections with Torsion in (Para-)complexified Structures ⋮ Complex nilmanifolds with constant holomorphic sectional curvature ⋮ Some recent progress in non-Kähler geometry ⋮ Lie groups with flat Gauduchon connections ⋮ (Para-)holomorphic and conjugate connections on (para-)Hermitian and (para-)Kähler manifolds ⋮ On Gauduchon Kähler-like manifolds ⋮ Compact Hermitian surfaces with pointwise constant Gauduchon holomorphic sectional curvature ⋮ Complex nilmanifolds and Kähler-like connections ⋮ Scalar curvatures in almost Hermitian geometry and some applications ⋮ On Strominger space forms ⋮ On a variational theorem of Gauduchon and torsion-critical manifolds

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• Hermitian manifolds with zero curvature
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• On curvature tensors of Hermitian manifolds
• Minimal complex surfaces with Levi-Civita Ricci-flat metrics
• A class of compact, complex manifolds which are not algebraic
• Ricci curvatures on Hermitian manifolds
• Complex Parallisable Manifolds

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