论文标题
Levi-Civita连接的无效注射性
Null-projectability of Levi-Civita connections
论文作者
论文摘要
我们研究了沿着基础歧管上的叶面的无扭力连接的可突发性的自然特性，这导致了当地叶片空间上预计的无扭转连接，重点是沿叶子沿叶子沿叶的levi-civita连接沿叶子沿叶子沿叶子的较短分布，从而无效。对于中性度量签名和中期分布，AFIFI在1954年表明，Levi-Civita连接的可预测性在当地是Patterson和Walker's Riemann扩展指标的情况。我们将此对应关系扩展到任何维度的无空平行分布，并引入了Riemann扩展的合适概括。
We study the natural property of projectability of a torsion-free connection along a foliation on the underlying manifold, which leads to a projected torsion-free connection on a local leaf space, focusing on projectability of Levi-Civita connections of pseudo-Riemannian metric along foliations tangent to null parallel distributions. For the neutral metric signature and mid-dimensional distributions, Afifi showed in 1954 that projectability of the Levi-Civita connection characterizes, locally, the case of Patterson and Walker's Riemann extension metrics. We extend this correspondence to null parallel distributions of any dimension, introducing a suitable generalization of Riemann extensions.
