Hermitian metrics with vanishing second Chern Ricci curvature

2023/09/19 by Kyle Broder, Broder, Kyle, Artem Pulemotov +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #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.2309.10295

openalex publication_date 2023/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a rigidity phenomenon exhibited by the second Chern Ricci curvature of a Hermitian metric on a compact complex manifold. This yields a characterisation of second Chern Ricci-flat Hermitian metrics on several types of manifolds as well as a range of non-existence results for such metrics.

Related

• Hermitian metrics on complex non-Kähler manifolds
• The behavior of the second Ricci flow on complex parallelizable manifolds
• Deformation of Hermitian metrics
• Ricci Curvatures on Hermitian manifolds
• Manifolds with non-positive second Chern-Ricci curvature