紧李群的标准黎曼浸入的谱几何
The spectral geometry of the canonical Riemannian submersion of a compact Lie Group
摘要：
设G是一个紧连通李群，G具有双不变黎曼度量.设m（x，y）=xy为乘法算子。我们证明了相关的纤维化m映射G × G G G是一个黎曼淹没与全测地纤维，我们研究了这种淹没的谱几何。我们表明拉回的基础上的特征形有有限的傅里叶级数的全空间，我们给出的例子，任意多个傅里叶系数可以是非零的。给出了基上的形式的拉回在全空间上是调和的充要条件。
英文摘要：
Let G be a compact connected Lie group which is equipped with a bi-invariant Riemannian metric. Let m(x,y)=xy be the multiplication operator. We show the associated fibration m mapping GxG to G is a Riemannian submersion with totally geodesic fibers and we study the spectral geometry of this submersion. We show the pull back of eigenforms on the base have finite Fourier series on the total space and we give examples where arbitrarily many Fourier coefficients can be non-zero. We give necessary and sufficient conditions that the pull back of a form on the base is harmonic on the total space.
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