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Geodesics and the geometry of manifolds. (English) Zbl 1316.53048

Summary: In this paper contains some remarks regarding projectively related (metric) connections on a 4-dimensional manifold, that is, Levi-Civita connections which yield the same paths for their (unparametrised) geodesics. Some techniques for such an investigation are briefly outlined. The signature of the metric is arbitrary but special emphasis is laid on the Lorentz case and the connection with the Einstein principle of equivalence in general relativity theory. The results are based on joint work with David Lonie and Zhixiang Wang in Aberdeen.

MSC:

53C22 Geodesics in global differential geometry
53B10 Projective connections
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
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