Vol. 269, No. 2, 2014

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ISSN: 0030-8730
Hypersurfaces with prescribed angle function

Henrique F. de Lima, Eraldo A. Lima Jr. and Ulisses L. Parente

Vol. 269 (2014), No. 2, 393–406
Abstract

We deal with two-sided complete hypersurfaces immersed in a Riemannian product space, whose base is assumed to have sectional curvature bounded from below. In this setting, we obtain sufficient conditions which assure that such a hypersurface is a slice of the ambient space, provided that its angle function has some suitable behavior. Furthermore, we establish a natural relation between our results and the classical problem of describing the geometry of a hypersurface immersed in the Euclidean space through the behavior of its Gauss map.

Keywords
Riemannian product spaces, two-sided complete hypersurfaces, mean curvature, height function, entire vertical graphs
Mathematical Subject Classification 2010
Primary: 53C42
Secondary: 53C50, 53B30
Milestones
Received: 30 April 2013
Revised: 28 February 2014
Accepted: 4 March 2014
Published: 26 July 2014
Authors
Henrique F. de Lima
Departamento de Matemática
Universidade Federal de Campina Grande
Campina Grande-PB
58429-970
Brazil
Eraldo A. Lima Jr.
Departamento de Matemática
Universidade Federal do Ceará
Fortaleza-CE
60356-000
Brazil
Ulisses L. Parente
Faculdade de Educação, Ciências e Letras do Sertão Central
Universidade Estadual do Ceará
Quixadá-CE
63900-000
Brazil