论文标题
谐波空间上的谐波径向矢量场
Harmonic radial vector fields on harmonic spaces
论文作者
论文摘要
我们根据函数上拉普拉斯$δ^0 $的径向特征空间的各个空间的尺寸和1型上的laplacian $Δ^1 $来表征谐波空间。我们检查了奇异性的性质，因为大地距离$ r $倾向于将径向特征函数和1型的零零。通过二元性，我们的结果为径向矢量场带来了相应的结果。我们的许多结果扩展到空间的上下文，这些空间相对于一个点是谐波的。
We characterize harmonic spaces in terms of the dimensions of various spaces of radial eigen-spaces of the Laplacian $Δ^0$ on functions and the Laplacian $Δ^1$ on 1-forms. We examine the nature of the singularity as the geodesic distance $r$ tends to zero of radial eigen-functions and 1-forms. Via duality, our results give rise to corresponding results for radial vector fields. Many of our results extend to the context of spaces which are harmonic with respect to a single point.
