  In this paper, we characterize the system of left translates
$\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$, $g\in L^2(\mathbb{H})$, to be a frame
sequence or a \emph{Riesz} sequence in terms of the twisted translates of the
corresponding function $g^\lambda$. Here, $(\mathbb{H}$ denotes the Heisenberg
group and $g^\lambda$ the inverse Fourier transform of $g$ with respect to the
central variable. This type of characterization for a \emph{Riesz} sequence
allows us to find some concrete examples. We also study the structure of the
oblique dual of the system of left translates
$\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$ on $(\mathbb{H}$. This result is also
illustrated with an example.
