Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1511-1524.

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Kähler Immersions of Pseudoconvex Hartogs Domains into Complex Space Forms

Yihong Hao1,*(),An Wang2()   

  1. 1 Department of Mathematics, Northwest University, Xi'an 710127
    2 School of Mathematical Sciences, Capital Normal University, Beijing 100048
  • Received:2019-05-24 Online:2020-12-26 Published:2020-12-29
  • Contact: Yihong Hao;
  • Supported by:
    the NSFC(11601422);the NSFC(11671270);the NSFC(11871044);the Beijing Municipal Natural Science Foundation(1182008);the NSF of Hebei Province(A2019106037);the NSF of Shannxi Province(2019JQ-398);the Scientific Research Program of Shaanxi Provincial Education Department(19JK0841);the Science Research Foundation of Northwest University(15NW23)


Let $\Omega$ be a bounded pseudoconvex Hartogs domain in ${\Bbb C}^{n}$. There exists a natural Kähler metric $g^{\Omega}$ in terms of its defining function. In this paper, we study the existence of Kähler immersions of $(\Omega, h g^{\Omega})$ into finite and infinite dimensional complex space forms for $h>0$.

Key words: Kähler immersion, Complex space form, Pseudoconvex Hartogs domain

CLC Number: 

  • O174.5