Spacelike graphs with parallel mean curvature

We consider spacelike graphs ${\mathrm{\Gamma }}_f$ of simple products $(M\times N, g\times -h)$where$(M,g)$and$(N,h)$areRiemannianmanifoldsand$f:M\to N$isasmoothmap\mathrm{.}UndertheconditionoftheCheegerconstantof$M$ to be zero and some condition on the second fundamental form at infinity, we conclude that if ${\mathrm{\Gamma }}_f\subset M\times N$ has parallel mean curvature $H$ then $H=0$. This holds trivially if $M$ is closed. If $M$ is the $m$-hyperbolic space then for any constant $c$, we describe a explicit foliation of $H^m\times R$ by hypersurfaces with constant mean curvature $c$.