On the curvature of tensor product connections and covariant differentials
Janyška, Josef
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Janyška, Josef
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Dussan, Martha, Noronha, Maria Helena (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Izu Vaisman (1968)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Eric Boeckx, Lieven Vanhecke (2001)
Czechoslovak Mathematical Journal
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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.