On the quadric CMC spacelike hypersurfaces in Lorentzian space forms

Cícero P. Aquino, Henrique F. de Lima, and Fábio R. dos Santos. "On the quadric CMC spacelike hypersurfaces in Lorentzian space forms." Colloquium Mathematicae 145.1 (2016): 89-98. <http://eudml.org/doc/286616>.

@article{CíceroP2016,
abstract = {We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.},
author = {Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos},
journal = {Colloquium Mathematicae},
keywords = {lorentzian space forms; complete spacelike hypersurfaces; totally umbilical hypersurfaces; hyperbolic cylinders; constant Mean curvature; support functions},
language = {eng},
number = {1},
pages = {89-98},
title = {On the quadric CMC spacelike hypersurfaces in Lorentzian space forms},
url = {http://eudml.org/doc/286616},
volume = {145},
year = {2016},
}

TY - JOUR
AU - Cícero P. Aquino
AU - Henrique F. de Lima
AU - Fábio R. dos Santos
TI - On the quadric CMC spacelike hypersurfaces in Lorentzian space forms
JO - Colloquium Mathematicae
PY - 2016
VL - 145
IS - 1
SP - 89
EP - 98
AB - We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.
LA - eng
KW - lorentzian space forms; complete spacelike hypersurfaces; totally umbilical hypersurfaces; hyperbolic cylinders; constant Mean curvature; support functions
UR - http://eudml.org/doc/286616
ER -