Totally umbilical hypersurfaces of manifolds admitting a unit Killing field
Differential Geometry
2010-07-09 v2
Abstract
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 satisfying this condition.
Keywords
Cite
@article{arxiv.1006.1261,
title = {Totally umbilical hypersurfaces of manifolds admitting a unit Killing field},
author = {Rabah Souam and Joeri Van der Veken},
journal= {arXiv preprint arXiv:1006.1261},
year = {2010}
}
Comments
minor corrections to v1