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An application of Bochner's technique to the deformations of the complex structure of $\mathbb C \mathbb P^n$


Author: Yong Ouyang
Journal: Proc. Amer. Math. Soc. 131 (2003), 3703-3709
MSC (2000): Primary 32G05, 58J05
Published electronically: July 2, 2003
MathSciNet review: 1998177
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the deformation of the complex structure of $\mathbb C \mathbb P^n$. We show that a harmonic deformation on $\mathbb C \mathbb P^n$ equipped with the Fubini-Study metric is trivial if its supernorm is appropriately small.


References [Enhancements On Off] (What's this?)

  • 1. James Morrow and Kunihiko Kodaira, Complex manifolds, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1971. MR 0302937
  • 2. M. Kuranishi, New proof for the existence of locally complete families of complex structures, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 142–154. MR 0176496

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Additional Information

Yong Ouyang
Affiliation: Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, 130-012 Seoul, Korea
Address at time of publication: 510403, GuangZhou, Jin Zhong Heng Lu, BaiLan HuaYuan, 25 Dong 403, P. R. China
Email: ouyang@newton.kias.re.kr

DOI: https://doi.org/10.1090/S0002-9939-03-07126-0
Received by editor(s): January 6, 2002
Published electronically: July 2, 2003
Communicated by: Mohan Ramachandran
Article copyright: © Copyright 2003 American Mathematical Society