Existence of a complete holomorphic vector field via the\n K "ahler-Einstein metric

2020/11/27 by Young-Jun Choi, Choi, Young-Jun, Kang-Hyurk Lee +1
Mathematics · Physics and Astronomy · #32M05 #32Q20 #53C55 #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2011.13576

openalex publication_date 2020/11/27 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the existence of a complete holomorphic vector fields\non a strongly pseudoconvex complex manifold admitting a negatively curved\ncomplete K "ahler-Einstein metric and a discrete sequence of automorphisms.\nUsing the method of potential scaling, we will show that there is a potential\nfunction of the K "ahler-Einstein metric whose differential has a constant\nlength. Then we will construct a complete holomorphic vector field from the\ngradient vector field of the potential function.\n

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