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A Remark on Steinness*

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Abstract

In this paper, the authors prove that if M n is a complete noncompact Kähler manifold with a pole p, and its holomorphic bisectional curvature is asymptotically non-negative to p, then it is a Stein manifold.

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References

  1. 1.

    Ni, L. and Tam, L. F., Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature, J. Diff. Geom., 64, 2003, 457–524

  2. 2.

    Grauert, H., On Levi's problem and the embedding of real-analytic manifolds, Ann. of Math., 68, 1958, 460–472

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Author information

Correspondence to Chaohui Zhou.

Additional information

*Project supported by the National Natural Science Foundation of China (No. 10471105, No. 10571135).

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Zhou, C., Chen, Z. A Remark on Steinness*. Chin. Ann. Math. Ser. B 28, 161–164 (2007). https://doi.org/10.1007/s11401-005-0440-1

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Keywords

  • Holomorphic bisectional curvature
  • Plurisubharmonic
  • Smooth
  • Exhausting

2000 MR Subject Classification

  • 58G11