Twistor Theory for Riemannian Symmetric Spaces
Twistor Theory for Riemannian Symmetric Spaces
复制标题
黎曼对称空间的扭转理论
DOI：
10.1007/bfb0095561
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
J. Rawnsley
中科院分区：
文献类型：
--
作者：
F. Burstall;J. Rawnsley
在这本关于扭转理论及其在调和映射理论中的应用的专著中，一个中心主题是旗流形的复杂齐次几何与对称空间的真实齐次几何之间的相互作用。特别地，标志流形显示为黎曼对称空间的扭曲空间。该理论的应用包括黎曼对称空间中稳定调和2球的完全分类和李群中调和2球的Bäcklund变换，在许多情况下，该变换为这类球和间隙现象提供了分解定理。所用的主要方法是齐次几何和李论以及黎曼曲面的一些代数几何。这项工作针对微分几何学者，特别是那些对最小曲面和齐次流形感兴趣的学者。
In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Riemannian symmetric spaces. Applications of this theory include a complete classification of stable harmonic 2-spheres in Riemannian symmetric spaces and a Bäcklund transform for harmonic 2-spheres in Lie groups which, in many cases, provides a factorisation theorem for such spheres as well as gap phenomena. The main methods used are those of homogeneous geometry and Lie theory together with some algebraic geometry of Riemann surfaces. The work addresses differential geometers, especially those with interests in minimal surfaces and homogeneous manifolds.