New Characterization of Pseudo-holomorphic Curves in CPn in Terms of the An-Toda Equations

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New Characterization of Pseudo-holomorphic Curves in CPⁿ in Terms of the A_n-Toda Equations

MO Xiaohuan

School of Mathematical Sciences, Peking University, Beijing, 100871

Received:1997-04-28 Online:1998-09-20 Published:1998-09-20

CPⁿ中伪全纯曲线的A_n-Toda方程刻划

莫小欢

北京大学数学学院，北京，100871

Abstract

Abstract: The relation between solutions of the Toda equations for SU(n+1) and pseudo-holomorphicity of the harmonic surfaces in CPⁿ are given. We show that any harmonic two-spheres in CPⁿ give a solution to the A_n-Toda equations.

Key words: complex projective space, A_n-Toda equation, Pseudo-holomorphic curves

摘要： 给出了对于SU(n+1)的Toda方程与CPⁿ中调和曲面的伪全纯性的关系。并证得了CPⁿ中每一2维调和球给出了A_n-Toda方程的解。

关键词: 复射影空间, A_n-Toda方程, 伪全纯曲线

CLC Number:

O186.16

MO Xiaohuan. New Characterization of Pseudo-holomorphic Curves in CPⁿ in Terms of the A_n-Toda Equations[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

莫小欢. CPⁿ中伪全纯曲线的A_n-Toda方程刻划[J]. 北京大学学报（自然科学版）.

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URL: https://xbna.pku.edu.cn/EN/

https://xbna.pku.edu.cn/EN/Y1998/V34/I5/574

[1]	YE Pingkai,MO Xiaohuan,SUN Fang. Harmonic Morphisms into Almost Hermitian Manifolds [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2006, 42(1): 35-40.
[2]	ZANG Yingyun,CHEN Weihuan. The Spectral Transformation of CMC Surfaces in S³ [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2005, 41(1): 36-46.
[3]	WEN Guochun. The Riemann-Hilbert Problem for Linear Degenerate Elliptic Complex Equations of First Order [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2005, 41(1): 47-54.
[4]	MO Xiaohuan. Harmonic Two spheres in CPⁿ with Antipodal Symmetry and Complementation [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1997, 33(3): 273-281.
[5]	MO Xiaohuan. A Characterization of Harmonic Surfaces in CPⁿ with Special Constant Kähler Angle [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1995, 31(3): 277-281.

New Characterization of Pseudo-holomorphic Curves in CPⁿ in Terms of the A_n-Toda Equations

CPⁿ中伪全纯曲线的A_n-Toda方程刻划

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