2026-06-01T01:11:12Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/227812026-02-03T11:08:29Zcom_10630_2254col_10630_37953

Mean curvature of spacelike submanifolds in a Brinkmann spacetime Cánovas, Verónica L. Romero, Alfonso Palomo-Ruiz, Francisco José Matemáticas aplicadas Geometría Brinkmann 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. 2021-09-02T11:17:03Z 2021-09-02T11:17:03Z 2021 2021 journal article https://hdl.handle.net/10630/22781 eng open access