论文标题
谎言群和复杂值的谐波形态上的保形叶子
Conformal foliations on Lie groups and complex-valued harmonic morphisms
论文作者
论文摘要
我们研究了Riemannian Lie coupt $ g $ g $ a子组$ k $生成的Riemannian Lie gubs $ \ Mathcal {f} $。我们对这种叶子感兴趣，这些叶子是保形的，并且对二次拟构叶的叶子最小。当子组$ k $是重要的$ \ textbf {su}（2）（2）\ times \ textbf {su}（2）$，$ \ textbf {su}（su}（su}（su}（2）\ times \ times \ textbf {sl} _2（sl} _2）， $ \ textbf {su}（2）\ times \ textbf {so}（2）$或$ \ textbf {sl} _2（\ Mathbb {r}）\ times \ times \ textbf {so}（so}（2）$。通过此，我们在每种情况下产生了新的谎言组的多维家族$ g $。这些叶子$ \ MATHCAL {F} $在相应的Lie Group $ G $上产生本地复杂值的谐波形态。
We study left-invariant foliations $\mathcal{F}$ on Riemannian Lie groups $G$ generated by a subgroup $K$. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations $\mathcal{F}$ when the subgroup $K$ is one of the important $\textbf{SU}(2)\times\textbf{SU}(2)$, $\textbf{SU}(2)\times\textbf{SL}_2(\mathbb{R})$, $\textbf{SU}(2)\times\textbf{SO}(2)$ or $\textbf{SL}_2(\mathbb{R})\times\textbf{SO}(2)$. By this we yield new multi-dimensional families of Lie groups $G$ carrying such foliations in each case. These foliations $\mathcal{F}$ produce local complex-valued harmonic morphisms on the corresponding Lie group $G$.
