  The topology of isoenergetic surfaces in reciprocal space for simple (sc),
body-centered (bcc), and face-centered (fcc) cubic lattices is investigated in
detail in the tight-binding approximation, taking into account the transfer
integrals between the nearest and next neighbors $t$ and $t'$. It is shown
that, for values $\tau = t'/t = \tau_\ast$ corresponding to a change in the
topology of surfaces, lines and surfaces of $\mathbf k$-van Hove points can be
formed. With a small deviation of $\tau$ from these singular values, the
spectrum in the vicinity of the van Hove line (surface) is replaced by a weak
dependence on $\mathbf k$ in the vicinity of several van Hove points that have
a giant mass proportional to $|\tau - \tau_ \ast|^{-1}$. Singular contributions
to the density of states near peculiar $\tau$ values are considered; analytical
expressions for the density of states being obtained in terms of elliptic
integrals. It is shown that in a number of cases the maximum value of the
density of states is achieved at energies corresponding not to
$\mathbf{k}$-points on the Brillouin zone edges, but to its internal points in
highly symmetrical directions. The corresponding contributions to electron and
magnetic properties are treated, in particular, in application to weak
itinerant magnets.
