RT Journal Article
T1 Mean curvature of spacelike submanifolds in a Brinkmann spacetime
A1 Cánovas, Verónica L.
A1 Romero, Alfonso
A1 Palomo-Ruiz, Francisco José
K1 Matemáticas aplicadas
K1 Geometría
K1 Brinkmann
AB Several geometric properties of complete spacelike submanifolds, with codimension at least two, in a Brinkmann spacetime are shown from natural assumptions involving the mean curvature vector field  $\mcv$ of the spacelike submanifold. Especially, we get sufficient conditions that assure that a spacelike submanifold is contained in a leaf of the foliation of the Brinkmann spacetime defined by the orthogonal vectors to the parallel lightlike vector field. When this vector field is the gradient of a smooth function, a characterization of arbitrary codimension spacelike submanifolds contained in a leaf of this foliation is given. In the case of plane fronted wave spacetimes, relevant examples of Brinkmann spacetimes that generalize pp-waves spacetimes, several uniqueness results for codimension two spacelike submanifolds are obtained. In particular, it is proven that any compact codimension two spacelike submanifold with $\mcv=0$ in a plane fronted spacetime wave must be a (totally geodesic) front of wave.
YR 2021
FD 2021
LK https://hdl.handle.net/10630/22781
UL https://hdl.handle.net/10630/22781
LA eng
NO The first author has been partially supported by MINECO/FEDER project MTM2015-65430-P, Fundaci\'on S\'eneca project 19901/GERM/15 and research grant 19783/FPI/15 from Fundaci\'on S\'eneca, the second and the third authors by Spanish MINECO and ERDF project MTM2016-78807-C2-1-P and Andalusian and ERDF project A-FQM-494-UGR18
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 29 ene 2026