Examples of Thomas-Whitehead projective connections
Projective connections on a manifold can be represented by Thomas-Whitehead (TW) connections, which are just linear connections on a natural \(\mathbb{R}\)-bundle over the manifold satisfying certain special properties. We show that 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-connections for a homogeneous space.
scientific article; zbMATH DE number 1145936