Existence of twisted constant scalar curvature Kähler metrics with a large twist

  title={Existence of twisted constant scalar curvature K{\"a}hler metrics with a large twist},
  author={Y. Hashimoto},
  journal={Mathematische Zeitschrift},
  • Y. Hashimoto
  • Published 2015
  • Mathematics
  • Mathematische Zeitschrift
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… Expand
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