Complete foliations of space forms by hypersurfaces |
| |
Authors: | A Caminha P Souza F Camargo |
| |
Institution: | 1. Departamento de Matemática, Universidade Federal do Ceará, 60455-760, Fortaleza, CE, Brazil 2. Departamento de Matemática, Universidade Federal do Piauí, 64049-550, Teresina, PI, Brazil 3. Departamento de Matemática, Universidade Federal de Campina Grande, 58109-970, Campina Grande, PB, Brazil
|
| |
Abstract: | We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures.
In particular, in Euclidean space we obtain a Bernstein-type theorem for graphs whose mean and scalar curvature do not change
sign but may otherwise be nonconstant. We also establish the nonexistence of foliations of the standard sphere whose leaves
are complete and have constant scalar curvature, thus extending a theorem of Barbosa, Kenmotsu and Oshikiri. For the more
general case of r-minimal foliations of the Euclidean space, possibly with a singular set, we are able to invoke a theorem of Ferus to give
conditions under which the non- singular leaves are foliated by hyperplanes. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|