On almost nonpositive $k$-Ricci curvature
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Publication:6375847
DOI10.1007/S12220-022-01055-2arXiv2108.10237MaRDI QIDQ6375847
Publication date: 23 August 2021
Abstract: Motivated by the recent work of Chu-Lee-Tam on the nefness of canonical line bundle for compact K"{a}hler manifolds with nonpositive -Ricci curvature, we consider a natural notion of {em almost nonpositive -Ricci curvature}, which is weaker than the existence of a K"{a}hler metric with nonpositive -Ricci curvature. When , 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 -Ricci curvature bounded from above by a positive constant. As an application, we prove that a compact K"{a}hler manifold of almost nonpositive -Ricci curvature must have nef canonical line bundle.
Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Negative curvature complex manifolds (32Q05) Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) (53E30)
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