Geodesic
Unit tangent sphere bundles with constant scalar curvature
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 523-544 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 53C25
Keywords: unit tangent sphere bundles; constant scalar curvature; Einstein and Ricci-parallel metrics 
@article{CMJ_2001_51_3_a6,
     author = {Boeckx, E. and Vanhecke, L.},
     title = {Unit tangent sphere bundles with constant scalar curvature},
     journal = {Czechoslovak Mathematical Journal},
     pages = {523--544},
     year = {2001},
     volume = {51},
     number = {3},
     mrnumber = {1851545},
     zbl = {1079.53063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a6/}
}
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Boeckx, E.; Vanhecke, L. Unit tangent sphere bundles with constant scalar curvature. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 523-544. http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a6/