Entire bounded constant mean curvature Killing graphs
We show that under certain curvature conditions of the ambient space an entire Killing graph of constant mean curvature lying inside a slab must be a totally geodesic slice.
math.DG↗
arXiv subjects
J. H. de Lira
Publications and source records attributed to J. H. de Lira.
Closed Weingarten hypersurfaces in warped product manifolds
Given a compact Riemannian manifold $M$, we consider a warped product $\bar M = I \times_h M$ where $I$ is an open interval in $\Rr$. We suppose that the mean curvature of the fibers do not change sign. Given a positive differentiable function $ψ$ in $\bar M$, we find a closed hypersurface $Σ$ which is solution of an equation of the form $F(B)=ψ$, where $B$ is the second fundamental form of $Σ$ and $F$ is a function satisfying certain structural properties. As examples, we may exhibit examples of hypersurfaces with prescribed higher order mean curvature.
math.DG↗
Existence of isometric immersions into nilpotent Lie groups
We establish necessary and sufficient conditions for existence of isometric immersions of a simply connected Riemannian manifold into a two-step nilpotent Lie group. This comprises the case of immersions into $H$-type groups.
math.DG↗
Helicoidal graphs with prescribed mean curvature
We prove an existence result for helicoidal graphs with prescribed mean curvature in a large class of warped product spaces which comprises space forms.
math.DG↗