论文标题
在曲折几乎复杂的结构上
On Twistor Almost Complex Structures
论文作者
论文摘要
在本文中，我们研究了两个天然几乎复杂的结构的可集成性问题$ j^{\ pm} _ \ nabla $在Twistor space $ j（m，g）上定义的均值差异$ m $，带有其他结构$ g $和$ g $和$ \ nabla $ a $ a $ g $ g $ -g $ -contection。我们还查看了$ j^{\ pm} _ \ nabla $的兼容性问题，其自然封闭$ 2 $ - form $ω^{j（m，g，\ nabla）} $在$ j（m，g）$上定义。对于$（m，g）$，我们考虑使用Levi civita连接或具有给定的符号连接$ \ nabla $的伪 - riemannian歧管，无论是否定向或不定位。在所有情况下，$ j（m，g）$都是与$ g $兼容的切线空间上的一堆复杂结构，我们用$π\ colon j（m，g）\ longrightArrow m $表示束投影。在以$ m $为导向的情况下，我们要求复杂结构的方向为给定。在符合性的情况下，复杂的结构为正。
In this paper we look at the question of integrability, or not, of the two natural almost complex structures $J^{\pm}_\nabla$ defined on the twistor space $J(M,g)$ of an even-dimensional manifold $M$ with additional structures $g$ and $\nabla$ a $g$-connection. We also look at the question of the compatibility of $J^{\pm}_\nabla$ with a natural closed $2$-form $ω^{J(M,g,\nabla)}$ defined on $J(M,g)$. For $(M,g)$ we consider either a pseudo-Riemannian manifold, orientable or not, with the Levi Civita connection or a symplectic manifold with a given symplectic connection $\nabla$. In all cases $J(M,g)$ is a bundle of complex structures on the tangent spaces of $M$ compatible with $g$ and we denote by $π\colon J(M,g) \longrightarrow M$ the bundle projection. In the case $M$ is oriented we require the orientation of the complex structures to be the given one. In the symplectic case the complex structures are positive.
