Jacobi Fields Along Harmonic 2‐Spheres in CP2 are Integrable
Jacobi Fields Along Harmonic 2‐Spheres in CP2 are Integrable
复制标题
CP2 中沿调和 2-球面的雅可比场是可积的
DOI：
10.1112/s0024610702003496
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
J. Wood
中科院分区：
文献类型：
--
作者：
L. Lemaire;J. Wood
本文证明了从2球到复射影平面沿调和映射的任何雅可比场都是可积的（即与调和映射的光滑变分相切）。这为可积性问题提供了为数不多的已知答案之一，该问题是在不同的几何和分析背景下提出的。这意味着雅可比场构成了S2到CP2调和映射流形的每个分量的切束，从而给出了任何调和映射的零；它还关系到从3 -流形到CP2在奇点附近的弱调和E -最小化映射的行为，以及从任意流形到CP2的弱调和E -最小化映射的奇异集的结构。
The paper shows that any Jacobi field along a harmonic map from the 2‐sphere to the complex projective plane is integrable (that is, is tangent to a smooth variation through harmonic maps). This provides one of the few known answers to the problem of integrability, which was raised in different contexts of geometry and analysis. It implies that the Jacobi fields form the tangent bundle to each component of the manifold of harmonic maps from S2 to CP2 thus giving the nullity of any such harmonic map; it also has a bearing on the behaviour of weakly harmonic E‐minimizing maps from a 3‐manifold to CP2 near a singularity and the structure of the singular set of such maps from any manifold to CP2.