Morse Theory and Infinite Families¶of Harmonic Maps Between Spheres
Morse Theory and Infinite Families¶of Harmonic Maps Between Spheres
复制标题
莫尔斯理论和球体之间调和图的无限族¶
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
R. Wald
中科院分区：
文献类型：
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作者：
K. Corlette;R. Wald
翻译后摘要：Bizobalet和Chmaj证明了存在一个无限序列的调和映射之间的领域的某些方面。这个序列与爱因斯坦-杨-米尔斯方程的解的Bartnik-McKinnon序列以及其他物理模型中出现的解的序列有许多共同的特征。利用莫尔斯理论方法证明了调和映射序列的存在性，并证明了该序列的某些指数和收敛性。此外，我们推广了Bizoirs和Chmaj的结果，以产生以前不知道的调和映射的无穷序列。序列的存在性和性质的关键特征“负责”，从而被视为存在反射（π 2）对称性和存在无限指数的奇异调和映射，这是在这种对称性下不变的。
Abstract: Existence of an infinite sequence of harmonic maps between spheres of certain dimensions was proven by Bizoń and Chmaj. This sequence shares many features of the Bartnik–McKinnon sequence of solutions to the Einstein–Yang–Mills equations as well as sequences of solutions that have arisen in other physical models. We apply Morse theoretic methods to prove existence of the harmonic map sequence and to prove certain index and convergence properties of this sequence. In addition, we generalize the result of Bizoń and Chmaj to produce infinite sequences of harmonic maps not previously known. The key features “responsible” for the existence and properties of the sequence are thereby seen to be the presence of a reflection (ℤ2) symmetry and the existence of a singular harmonic map of infinite index which is invariant under this symmetry.