论文标题
偏向四个维度的杀死纺纱器
Skew Killing spinors in four dimensions
论文作者
论文摘要
本文致力于携带偏斜杀手的4维里曼式旋转歧管的分类。一个偏斜的杀伤旋转器$ψ$是一个满足方程式$ \ nabla $ x $ x $ = ax $ = ax $ \ times $ $ $ψ$的旋转器，带有偏斜的符合符号的内态A。我们考虑了脱位案例，其中a的排名最多是两种，最多有两个案例，而非分数则无处不在。我们证明，在退化的情况下，歧管在riemannian乘积r x n的局部等轴测图中具有偏斜的杀伤旋转器，我们在旋转器上解释了哪些条件是局部等轴测局的特殊情况，即S 2 x r 2的特殊情况。在非分类的情况下，偏斜杀伤旋转器的存在与我们将描述的数据定义数据有关。
This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor $ψ$ is a spinor that satisfies the equation $\nabla$X$ψ$ = AX $\times$ $ψ$ with a skew-symmetric endomorphism A. We consider the degenerate case, where the rank of A is at most two everywhere and the non-degenerate case, where the rank of A is four everywhere. We prove that in the degenerate case the manifold is locally isometric to the Riemannian product R x N with N having a skew Killing spinor and we explain under which conditions on the spinor the special case of a local isometry to S 2 x R 2 occurs. In the non-degenerate case, the existence of skew Killing spinors is related to doubly warped products whose defining data we will describe.
