Scalar curvatures in almost Hermitian geometry and some applications

2019/01/29 by Jixiang Fu, Fu, Jixiang, Xianchao Zhou +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1901.10130

openalex publication_date 2019/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On an almost Hermitian manifold, we have two Hermitian scalar curvatures with respect to any canonical Hermitian connection defined by P. Gauduchon. Explicit formulas of these two Hermitian scalar curvatures are obtained in terms of Riemannian scalar curvature, norms of decompositions of covariant derivative of the fundamental 2-form with respect to the Levi-Civita connection, and the codifferential of the Lee form. Then we get some inequalities of various total scalar curvatures and some characterization results of the Kähler metric, balanced metric, locally conformally Kähler metric and the k-Gauduchon metric. As corollaries, we show some results related to a problem given by Lejmi-Upmeier \citeLeU and a conjecture given by Angella-Otal-Ugarte-Villacampa \citeAOUV.

Cited by

• Constant holomorphic sectional curvature conjecture and Fino-Vezzoni conjecture
• On Kodaira dimension and scalar curvature in almost Hermitian geometry
• Comparison theorems in Hermitian geometry I
• Conformal extremal metrics and constant scalar curvature

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