In this paper, we introduce a geometric flow for Kähler metrics $\omega_t$ coupled with closed $(1,1)$‑forms $\alpha_t$ on a compact Kähler manifold, whose stationary solution is a constant scalar curvature Kähler (cscK) metric, coupled with a harmonic $(1,1)$‑form. We establish the long-time existence, i.e., assuming the initial $(1,1)$‑form $\alpha$ is nonnegative, then the flow exists as long as the norm of the Riemannian curvature tensors are bounded.

中文翻译：

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Kähler流形上的新几何流

在本文中，我们介绍了Kähler度量$ \ omega_t $的几何流以及紧致Kähler流形上封闭的$（1,1）$形式$ \ alpha_t $的几何流，其固定解是恒定的标量曲率Kähler（cscK）度量，再加上谐波$（1,1）$形式。我们建立了长期存在，即，假设初始$（1,1）$形式的$ \ alpha $是非负的，那么只要黎曼曲率张量的范数有界，该流就存在。