The form-type Calabi-Yau equation on a class of complex manifolds
数学专题报告
报告题目(Title)：The form-type Calabi-Yau equation on a class of complex manifolds
报告人(Speaker)：黄立鼎（厦门大学）
地点(Place)：腾讯会议：370-673-641
时间(Time)：2024年7月1日（周一）上午9:30-11:00
邀请人(Inviter)：张科伟
报告摘要
The Calabi-Yau theorem says that given any smooth representative $\Phi$ of the first Chern class, there exists a unique K\”ahler metric $\omega$ cohomologous to $\alpha$ such that $Ricci(\omega)=\Phi$. It is natural to investigate whether similar results hold when the manifolds is non-K\”adler. In this talk, we will introduce the form type Calabi-Yau equation which can used to prove a version of the Calabi conjecture holds for balanced metrics. We define the astheno-Ricci curvature and prove that there exists a solution for the form type Calabi-Yau equation if the astheno-Ricci curvature is non-positive.
