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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Pseudo-holomorphic curves in complex Grassmann manifolds


Authors: Xiaoxiang Jiao and Jiagui Peng
Journal: Trans. Amer. Math. Soc. 355 (2003), 3715-3726
MSC (2000): Primary 53C42, 53C55
Published electronically: May 7, 2003
MathSciNet review: 1990170
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Abstract: It is proved that the Kähler angle of the pseudo-holomorphic sphere of constant curvature in complex Grassmannians is constant. At the same time we also prove several pinching theorems for the curvature and the Kähler angle of the pseudo-holomorphic spheres in complex Grassmannians with non-degenerate associated harmonic sequence.


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Additional Information

Xiaoxiang Jiao
Affiliation: Department of Mathematics, Graduate School, Chinese Academy of Sciences, Beijing 100039, China
Email: xxj@gscas.ac.cn

Jiagui Peng
Affiliation: Department of Mathematics, Graduate School, Chinese Academy of Sciences, Beijing 100039, China
Email: pengck@gscas.ac.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03244-6
PII: S 0002-9947(03)03244-6
Keywords: Gauss curvature, K\"{a}hler angle, harmonic sequence, pseudo-holomorphic curve
Received by editor(s): September 6, 2002
Received by editor(s) in revised form: October 31, 2002
Published electronically: May 7, 2003
Additional Notes: Supported by the National Natural Science Foundation of China (Grants No. 10001033, 10131020, 10071804) and the President Foundation of the Graduate School of the Chinese Academy of Sciences
Article copyright: © Copyright 2003 American Mathematical Society