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Title in Portuguese: On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces
Author: Colares, Antônio Gervásio
Palmas Velasco, Oscar Alfredo
Keywords: Curvatura
Variedades riemanianas
Issue Date: 2011
Citation: COLARES, A. G. ; PALMAS VELASCO, O. A. (2011)
Abstract: 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.
Description: COLARES, Antônio Gervásio ; PALMAS VELASCO, Oscar Alfredo. On Riemannian manifolds foliated by (n − 1)-umbilical hypersurfaces. Bulletin Brazilian Mathematical Society, v. 42, n. 1, p. 105-130, 2011.
Appears in Collections:DMAT - Artigos publicados em revista científica

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