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Suppose that there exist two Kähler metrics $$\omega $$ω and $$\alpha $$α such that the metric contraction of $$\alpha $$α with respect to $$\omega $$ω is constant, i.e. $$\varLambda _{\omega }… Click to show full abstract
Suppose that there exist two Kähler metrics $$\omega $$ω and $$\alpha $$α such that the metric contraction of $$\alpha $$α with respect to $$\omega $$ω is constant, i.e. $$\varLambda _{\omega } \alpha = \text {const}$$Λωα=const. We prove that for all large enough $$R>0$$R>0 there exists a twisted constant scalar curvature Kähler metric $$\omega '$$ω′ in the cohomology class $$[ \omega ]$$[ω], satisfying $$S(\omega ' ) - R \varLambda _{\omega ' } \alpha = \text {const}$$S(ω′)-RΛω′α=const. We discuss its implication to K-stability and the continuity method recently proposed by Chen.
Journal Title: Mathematische Zeitschrift
Year Published: 2018
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