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On almost nonpositive $k$-Ricci curvature

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 نشر من قبل Kai Tang
 تاريخ النشر 2021
  مجال البحث
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 تأليف Kai Tang




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Motivated by the recent work of Chu-Lee-Tam on the nefness of canonical line bundle for compact K{a}hler manifolds with nonpositive $k$-Ricci curvature, we consider a natural notion of {em almost nonpositive $k$-Ricci curvature}, which is weaker than the existence of a K{a}hler metric with nonpositive $k$-Ricci curvature. When $k=1$, this is just the {em almost nonpositive holomorphic sectional curvature} introduced by Zhang. We firstly give a lower bound for the existence time of the twisted K{a}hler-Ricci flow when there exists a K{a}hler metric with $k$-Ricci curvature bounded from above by a positive constant. As an application, we prove that a compact K{a}hler manifold of almost nonpositive $k$-Ricci curvature must have nef canonical line bundle.



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