Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds

Symmetry, Integrability and Geometry: Methods and Applications

关键词: projective structure;    holonomy;    Lorentz manifolds;    geodesic equivalence;   

DOI  :  

来源: DOAJ

【 摘 要 】

A study is made of 4-dimensional Lorentz manifolds which are projectively related, that is, whose Levi-Civita connections give rise to the same (unparameterised) geodesics. A brief review of some relevant recent work is provided and a list of new results connecting projective relatedness and the holonomy type of the Lorentz manifold in question is given. This necessitates a review of the possible holonomy groups for such manifolds which, in turn, requires a certain convenient classification of the associated curvature tensors. These reviews are provided.

【 授权许可】

Unknown