紧致 Hermitian 流形上的形变 Gauduchon-Yamabe 问题
Deformed Gauduchon-Yamabe problems on compact Hermitian manifolds
- Università degli Studi di Firenze（佛罗伦萨大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究紧致 Hermitian 流形上 Gauduchon 联络的标量曲率形变，给出常曲率度量存在判据，并分析 Yamabe 不变量的全局依赖性及临界阈值应用。
AI中文摘要：
我们研究了紧致 Hermitian 流形上与 Gauduchon 联络相关的标量曲率的双参数形变。一个核心恒等式通过 Chern 联络的挠率的无迹部分的平方范数表达了该形变对标量曲率对联络参数的依赖性。我们建立了常形变标量曲率度量的存在性判据，并分析了形变 Yamabe 不变量对联络参数的全局依赖性，包括达到临界阈值的情形。我们还研究了正共形类中的预定曲率问题。应用包括在至少二维的每个复维数中一个显式 Hopf 例子以及非局部共形 Kähler Iwasawa 乘积上达到临界阈值。
英文摘要：
We study a two-parameter deformation of scalar curvature associated with the Gauduchon connections on compact Hermitian manifolds. A central identity expresses its dependence on the connection parameter through the squared norm of the trace-free part of the torsion of the Chern connection. We establish existence criteria for metrics of constant deformed scalar curvature and analyze the global dependence of the deformed Yamabe invariant on the connection parameter, including when the critical threshold is reached. We also study a prescribed-curvature problem in positive conformal classes. Applications include attainment of the critical threshold for an explicit Hopf example in every complex dimension at least two and on non-locally conformally Kähler Iwasawa products.
