  The supercooled dynamics of a Lennard-Jones model liquid is numerically
investigated studying relevant points of the potential energy surface, i.e. the
minima of the square gradient of total potential energy $V$. The main findings
are: ({\it i}) the number of negative curvatures $n$ of these sampled points
appears to extrapolate to zero at the mode coupling critical temperature $T_c$;
({\it ii}) the temperature behavior of $n(T)$ has a close relationship with the
temperature behavior of the diffusivity; ({\it iii}) the potential energy
landscape shows an high regularity in the distances among the relevant points
and in their energy location. Finally we discuss a model of the landscape,
previously introduced by Madan and Keyes [J. Chem. Phys. {\bf 98}, 3342
(1993)], able to reproduce the previous findings.
