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Keywords:
unit tangent sphere bundles; constant scalar curvature; Einstein and Ricci-parallel metrics
unit tangent sphere bundles; constant scalar curvature; Einstein and Ricci-parallel metrics
Summary:
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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