Illinois Journal of Mathematics

A simple proof of a theorem of Calabi

Xiaojun Huang and Xiaoshan Li

Full-text: Open access

Abstract

We give a simple and more or less elementary proof of a classical result of E. Calabi on the global extension of a local holomorphic isometry into a complex space form.

Article information

Source
Illinois J. Math., Volume 56, Number 1 (2012), 95-99.

Dates
First available in Project Euclid: 27 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1380287462

Digital Object Identifier
doi:10.1215/ijm/1380287462

Mathematical Reviews number (MathSciNet)
MR3117020

Zentralblatt MATH identifier
1279.32009

Subjects
Primary: 32A 32D 32H 32M

Citation

Huang, Xiaojun; Li, Xiaoshan. A simple proof of a theorem of Calabi. Illinois J. Math. 56 (2012), no. 1, 95--99. doi:10.1215/ijm/1380287462. https://projecteuclid.org/euclid.ijm/1380287462


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References

  • S. Bochner and W. Martin, Several complex variables, Princeton University Press, Princeton, 1948.
  • E. Calabi, Isometric imbedding of complex manifolds, Ann. of Math. (2) 58 (1953), 1–23.
  • J. P. D'Angelo, Several complex variables and the geometry of real hypersurfaces, CRC Press, Boca Raton, FL, 1993.
  • X. Huang and Y. Yuan, Local holomorphic conformal maps between a class of Kähler manifolds; available at http://arxiv.org/abs/1305.3344.
  • N. Mok and S.-C. Ng, Germs of measure-preserving holomorphic maps from bounded symmetric domains to their Cartesian products, J. Reine Angew. Math. 669 (2012), 47–73.