Totally umbilical hypersurfaces of manifolds admitting a unit Killing field

  title={Totally umbilical hypersurfaces of manifolds admitting a unit Killing field},
  author={Rabah Souam and Joeri Van der Veken},
  journal={Transactions of the American Mathematical Society},
  • Rabah Souam, J. Veken
  • Published 2010
  • Mathematics
  • Transactions of the American Mathematical Society
We prove that a Riemannian product of type M x R (where R denotes the Euclidean line) admits totally umbilical hypersurfaces if and only if M has locally the structure of a warped product and we give a complete description of the totally umbilical hypersurfaces in this case. Moreover, we give a necessary and sufficient condition under which a Riemannian three-manifold carrying a unit Killing field admits totally geodesic surfaces and we study local and global properties of three-manifolds… Expand
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