A holonomy characterisation of Fefferman spaces
A holonomy characterisation of Fefferman spaces
复制标题
费弗曼空间的完整表征
DOI：
10.1007/s10455-010-9220-6
复制
发表时间：
2006
影响因子：
0.7
通讯作者：
A. R. Gover
中科院分区：
文献类型：
--
作者：
A. Čap;A. R. Gover
我们证明了与超曲面型非退化CR结构相联系的Fefferman空间是由标准牵引丛上平行正交复结构的存在刻画的，直到局部共形等距.这个条件可以用保角完整理论等价地表示出来。从这幅图中提取张量丛水平上的本质结果，产生了一个改进的、共形不变的类似于Sparling对Fefferman空间的刻画。
We prove that Fefferman spaces, associated to non-degenerate CR structures of hypersurface type, are characterised, up to local conformal isometry, by the existence of a parallel orthogonal complex structure on the standard tractor bundle. This condition can be equivalently expressed in terms of conformal holonomy. Extracting from this picture the essential consequences at the level of tensor bundles yields an improved, conformally invariant analogue of Sparling’s characterisation of Fefferman spaces.