A generalization of Berger's rigidity theorem for positively curved manifolds
Detlef Gromoll, Karsten Grove (1987)
Annales scientifiques de l'École Normale Supérieure
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Detlef Gromoll, Karsten Grove (1987)
Annales scientifiques de l'École Normale Supérieure
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Luis Guijarro, Peter Petersen (1997)
Annales scientifiques de l'École Normale Supérieure
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Isaac Chavel, Edgar A. Feldman (1974)
Compositio Mathematica
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Paweł Grzegorz Walczak (1984)
Annales Polonici Mathematici
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Deane Yang (1992)
Annales scientifiques de l'École Normale Supérieure
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Yun, Gabjin (2004)
International Journal of Mathematics and Mathematical Sciences
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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.