Article ID Journal Published Year Pages File Type
1893851 Journal of Geometry and Physics 2012 15 Pages PDF
Abstract

This paper considers the situation on a 4-dimensional manifold admitting two metric connections, one of which is compatible with a positive definite metric, and which have the same unparametrised geodesics. It shows how, in many cases, the relationship between these connections and metrics can be found. In many of these cases, the connections are found to be necessarily equal. The general technique used is that based on a certain classification of the curvature tensor together with holonomy theory.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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