Abstract
As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.
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Boeckx, E., Vanhecke, L. Unit Tangent Sphere Bundles with Constant Scalar Curvature. Czechoslovak Mathematical Journal 51, 523–544 (2001). https://doi.org/10.1023/A:1013779805244
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DOI: https://doi.org/10.1023/A:1013779805244