论文标题
一些伪-Kähler爱因斯坦$ 4 $ - 对称空间，带有“双”特殊复杂结构
Some pseudo-Kähler Einstein $4$-symmetric spaces with a "twin" special almost complex structure
论文作者
论文摘要
在$ 4 $ - 对称的符号空间，几乎不变的复杂结构 - 签名 - 成对出现。我们展示了约4美元的符号符号符号空间，其中一对“天然”兼容（通常不是积极的）几乎是复杂的结构，其中一个是可集成的，而另一个是最大不可集成的（即，在任何时候，其nijenhuis张量的图像在那时是整个切线空间）。该集成的一个定义了歧管上的伪卡勒爱因斯坦指标，而不可集成的是Ricci Hermitian（从某种意义上说，几乎复杂的结构保留了相关的Levi Civita连接的Ricci张量），而与之相关的Chern Ricci形式的意义上是相关形式的特殊形式。
On $4$-symmetric symplectic spaces, invariant almost complex structures -- up to sign -- arise in pairs. We exhibit some $4$-symmetric symplectic spaces, with a pair of "natural" compatible (usually not positive) invariant almost complex structures, one of them being integrable and the other one being maximally non integrable (i.e. the image of its Nijenhuis tensor at any point is the whole tangent space at that point). The integrable one defines a pseudo-Kähler Einstein metric on the manifold, and the non integrable one is Ricci Hermitian (in the sense that the almost complex structure preserves the Ricci tensor of the associated Levi Civita connection) and special in the sense that the associated Chern Ricci form is proportional to the symplectic form.
