Conformal Patterson–Walker metrics
Conformal Patterson–Walker metrics
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共形帕特森-沃克度量
DOI：
10.4310/ajm.2019.v23.n5.a1
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发表时间：
2016
影响因子：
0.6
通讯作者：
V. vZ'adn'ik
中科院分区：
文献类型：
--
作者：
M. Hammerl;Katja Sagerschnig;Josef vSilhan;Arman Taghavi;V. vZ'adn'ik
将经典的无扭仿射连接的分裂签名（伪）黎曼结构的Patterson-Walker构造推广到给定射影连接类的分裂签名共形结构的构造。得到了诱导结构的表征。我们在由Patterson-Walker度规构成的共形类中实现了爱因斯坦度规的完整描述。最后，我们描述了共形帕特森-沃克度规的所有对称性。在这两种情况下，我们都获得了原始结构的几何数据描述。
The classical Patterson-Walker construction of a split-signature (pseudo-)Riemannian structure from a given torsion-free affine connection is generalized to a construction of a split-signature conformal structure from a given projective class of connections. A characterization of the induced structures is obtained. We achieve a complete description of Einstein metrics in the conformal class formed by the Patterson-Walker metric. Finally, we describe all symmetries of the conformal Patterson-Walker metric. In both cases we obtain descriptions in terms of geometric data on the original structure.