论文标题
半摩曼谎言群体上的结晶最小叶子
Conformal Minimal Foliations on Semi-Riemannian Lie Groups
论文作者
论文摘要
我们研究了由亚组$ k $生成的半河畔谎言组$ g $ $ {\ MATHCAL F} $的左行叶。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。 We classify such foliations ${\mathcal F}$ when the subgroup $K$ is one of the important $\text{SU}(2)$, $\text{SL}_{2}(\mathbb R)$, $\text{SU}(2)\times\text{SU}(2)$, $ \ text {su}（2）\ times \ text {sl} _ {2}（\ mathbb r）$，$ \ text {su}（2）\ times \ times \ text {so}（so}（so}（2）$，$ \ text {sl {sl} _ {2} _ {2}（2}（\ mathbb r）这样，我们在每种情况下构建了谎言组的新的多维家族$ 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 semi-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 $\text{SU}(2)$, $\text{SL}_{2}(\mathbb R)$, $\text{SU}(2)\times\text{SU}(2)$, $\text{SU}(2)\times\text{SL}_{2}(\mathbb R)$, $\text{SU}(2)\times\text{SO}(2)$, $\text{SL}_{2}(\mathbb R)\times\text{SU}(2)$. This way we construct 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 $G$.
