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

DOI:
https://doi.org/10.1090/S0002-9947-03-03244-6

Published electronically:
May 7, 2003

MathSciNet review:
1990170

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-03-03244-6

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