Abstract
In this paper, we study the existence of a complete holomorphic vector field on a strongly pseudoconvex complex manifold admitting a negatively curved complete Kähler–Einstein metric and a discrete sequence of automorphisms. Using the method of potential scaling, we will show that there is a potential function of the Kähler–Einstein metric whose differential has a constant length. Then, we will construct a complete holomorphic vector field from the gradient vector field of the potential function.
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The research of first and second named authors was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (No. 2018R1C1B3005963, No. NRF-2019R1F1A1060891).
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Choi, YJ., Lee, KH. Existence of a complete holomorphic vector field via the Kähler–Einstein metric. Ann Glob Anal Geom 60, 97–109 (2021). https://doi.org/10.1007/s10455-021-09769-2
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DOI: https://doi.org/10.1007/s10455-021-09769-2