Prescribed Chern scalar curvatures on compact Hermitian manifolds with negative Gauduchon degree

DOI10.1016/J.JFA.2023.109948arXiv2208.08691MaRDI QIDQ6408182

Publication date: 18 August 2022

Abstract: In this paper, we investigate the problem of prescribing Chern scalar curvatures on compact Hermitian manifolds with negative Gauduchon degree. By studying the convergence of the associated geometric flow, we obtain some existence results when the candidate curvature function is nonzero and nonpositive. Furthermore, we also consider the case that the candidate curvature function is sign-changing, and establish some existence and nonexistence results.

Mathematics Subject Classification ID

Local differential geometry of Hermitian and Kählerian structures (53B35) Conformal structures on manifolds (53C18) Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) (53E30)

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