论文标题
紧凑的Weyl-Paralalel流形的新示例
New examples of compact Weyl-parallel manifolds
论文作者
论文摘要
我们证明了带有平行的Weyl张量的紧凑型伪riemannian歧管的存在，它们既不是固定的也不是局部对称的，并且代表了所有不确定的度量标志，在所有维度上$ \，n \ ge5 $。到目前为止，这种歧管仅在尺寸中存在$ \，n = 3j+2 $，其中$ \，j \，$是任何正整数[11]。与[11]一样，我们的示例是圆圈上的非平凡的圆环束，并源于用于适当选择的差异型欧亚人“模型”歧管的适当选择的离散等轴测组。
We prove the existence of compact pseudo-Riemannian manifolds with parallel Weyl tensor which are neither conformally flat nor locally symmetric, and represent all indefinite metric signatures in all dimensions $\,n\ge5$. Until now such manifolds were only known to exist in dimensions $\,n=3j+2$, where $\,j\,$ is any positive integer [11]. As in [11], our examples are diffeomorphic to nontrivial torus bundles over the circle and arise from a quotient-manifold construction applied to suitably chosen discrete isometry groups of diffeomorphically-Euclidean "model" manifolds.
