Hermitian metrics on complex non-Kähler manifolds

2025/03/21 by Daniele Angella, Angella, Daniele
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2503.16936

openalex publication_date 2025/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this survey, we consider various analytic problems related to the geometry of the Chern connection on Hermitian manifolds, such as the existence of metrics with constant Chern-scalar curvature, generalizations of the Kähler-Einstein condition to the non-Kähler setting, and the convergence of the Chern-Ricci flow on compact complex surfaces.

Related

• The Chern Sectional Curvature of a Hermitian Manifold
• Almost-Hermitian and Hermitian metrics
• An equivalence of scalar curvatures on Hermitian manifolds
• Hermitian metrics with vanishing second Chern Ricci curvature
• Homogeneous Hermitian manifolds and special metrics