论文标题
与叶子最小的共同叶的四维谎言基团上的自然几乎赫尔米尼亚结构
Natural Almost Hermitian Structures on Conformally Foliated 4-Dimensional Lie Groups with Minimal Leaves
论文作者
论文摘要
令$（g，g）$是一个4维里曼式的谎言组，带有二维左右，共形叶子$ \ mathcal {f} $，带有最小的叶子。让$ j $是$ g $几乎是一个适合叶子$ \ mathcal {f} $的hermitian结构。根据S. Gudmundsson和M. Svensson，相应的谎言代数$ \ mathfrak {g} $必须属于20个家庭之一$ \ mathfrak {g} _1，\ dots，\ mathfrak {g} _ {20} $。我们对几乎是Kähler$（\ Mathcal {a} \ Mathcal {k}）$的$ j $进行分类，intemable $（\ mathcal {i}）$或kähler$（\ mathcal {k}）$。在此，我们建造了16个多维的几乎是Kähler家庭，18个综合家庭和11个Kähler家庭。
Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $\mathcal{F}$ with minimal leaves. Let $J$ be an almost Hermitian structure on $G$ adapted to the foliation $\mathcal{F}$. The corresponding Lie algebra $\mathfrak{g}$ must then belong to one of 20 families $\mathfrak{g}_1,\dots,\mathfrak{g}_{20}$ according to S. Gudmundsson and M. Svensson. We classify such structures $J$ which are almost Kähler $(\mathcal{A}\mathcal{K})$, integrable $(\mathcal{I})$ or Kähler $(\mathcal{K})$. Hereby, we construct 16 multi-dimensional almost Kähler families, 18 integrable families and 11 Kähler families.
