Prescribed Chern scalar curvatures on complete Hermitian manifolds

2025/06/17 by Yu, Weike
#35J60 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.14592

Abstract

In this paper, we investigate the problem of prescribing Chern scalar curvatures on complete Hermitian manifolds. Firstly, we re-prove our recent result for prescribing sign-changing Chern scalar curvatures on compact Hermitian manifolds by using the classical maximum principle. Secondly, we study this problem on complete noncompact Hermitian manifolds, and generalize the Aviles-McOwen's existence results [J. Differential Geom., 21 (1985): 269-281] from Poincaré disks to higher dimensional Hermitian manifolds.

Citations

• Prescribed Chern scalar curvature flow on compact Hermitian manifolds with negative Gauduchon degree
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Related

• Hermitian metrics of constant Chern scalar curvature on ruled surfaces
• An equivalence of scalar curvatures on Hermitian manifolds
• Prescribing Chern scalar curvatures on noncompact manifolds
• The Chern Sectional Curvature of a Hermitian Manifold
• Prescribed Chern scalar curvature flow on compact Hermitian manifolds with negative Gauduchon degree