On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces

• Main Author: Colares, Antônio Gervásio
• Publication Date: 2011
• Other Authors: Velasco, Oscar Alfredo Palmas
• Format: Article
• Language: eng
• Source: Repositório Institucional da Universidade Federal do Ceará (UFC)
• Download full: http://www.repositorio.ufc.br/handle/riufc/4403
• topic: Curvatura; Hipersuperfícies; Variedades riemanianas

In this paper we define closed partially conformal vector fields and use them to give a characterization of Riemannian manifolds which admit this kind of fields as some special warped products foliated by (n − 1)-umbilical hypersurfaces. Examples are described in space forms. In particular, closed partially conformal vector fields in Euclidean spaces are associated to the most simple foliations given by hyperspheres, hyperplanes or coaxial cylinders. Finally, for manifolds admitting such vector fields, we impose conditions for a hypersurface to be (n − 1)-umbilical, or, in particular, a leaf of the corresponding foliation.