Main Article Content

Entire vertical graphs in Riemannian product spaces


Henrique Fernandes de Lima

Abstract

We extend the technique developed by S.T. Yau in [21] in order to investigate the rigidity of entire vertical graphs in a Riemannian product space R × Mn, whose fiber Mn is supposed to have Ricci curvature with strict sign. In this setting, under a suitable restriction on the norm of the gradient of the function u which determines such a graph Σn(u), we are able to prove that Σn(u) must be a slice {t} × Mn.

Keywords: Product spaces, entire vertical graphs, mean curvature, height function

Quaestiones Mathematicae 37(2014), 321–329

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606