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Examples of Thomas-Whitehead projective connections. (English) Zbl 0897.53009
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.

53B10 Projective connections
53C30 Differential geometry of homogeneous manifolds
53C05 Connections, general theory
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
Full Text: DOI
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