  This paper consists of two parts. First, motivated by classic results, we
determine the subsets of a given nilpotent Lie algebra $\mathfrak{g}$
(respectively, of the Grassmannian of two-planes of $\mathfrak{g}$) whose sign
of Ricci (respectively, sectional) curvature remains unchanged for an arbitrary
choice of a positive definite inner product on $\mathfrak{g}$. In the second
part we study the subsets of $\mathfrak{g}$ which are, for some inner product,
the eigenvectors of the Ricci operator with the maximal and with the minimal
eigenvalue, respectively. We show that the closures of these subsets is the
whole algebra $\mathfrak{g}$, apart from two exceptional cases: when
$\mathfrak{g}$ is two-step nilpotent and when $\mathfrak{g}$ contains a
codimension one abelian ideal.
