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math.DG2010★ 1 cited
Gauss maps of constant mean curvature surfaces in three-dimensional homogeneous spaces
Jun-ichi Inoguchi, Joeri Van der Veken
It is well-known that for a surface in a 3-dimensional real space form the constancy of the mean curvature is equivalent to the harmonicity of the Gauss map. However, this is not t…
math.DG2010
Totally umbilical hypersurfaces of manifolds admitting a unit Killing field
Rabah Souam, Joeri Van der Veken
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…