Abstract
Projective connections on a manifold can be represented by Thomas-Whitehead (TW) connections which are just linear connections on a natural R-bundle over the manifold satisfying certain special properties. We show TW-connections with recurrent curvature are flat, and we characterize the TW-connections which are metric connections. Finally, we classify invariant torsion-free linear connections, invariant projective structures, and invariant TW-conections for a homogeneous space.
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