  Properties, structure, and thermal evolution of neutron stars are determined
by the equation of state of stellar matter. Recent data on isospin-diffusion
and isoscaling in heavy-ion collisions at intermediate energies as well as the
size of neutron skin in $^{208}Pb$ have constrained considerably the density
dependence of the nuclear symmetry energy and, in turn, the equation of state
of neutron-rich nucleonic matter. These constraints could provide useful
information about the global properties of rapidly rotating neutron stars.
Models of rapidly rotating neutron stars are constructed applying several
nucleonic equations of state. Particular emphasis is placed on configurations
rotating rigidly at $716$ and $1122Hz$. The range of allowed hydrostatic
equilibrium solutions is determined and tested for stability. The effect of
rotation on the internal composition and thermal properties of neutron stars is
also examined. At a given rotational frequency, each equation of state yields a
range of possible neutron stars configurations restricted by the Keplerian
(mass-shedding) limit, corresponding to the maximal circumferential radius, and
the limit due to the onset of instabilities with respect to axial-symmetric
perturbations, corresponding to the minimal equatorial radius of a stable
neutron star model. We show that the mass of a neutron star rotating uniformly
at $1122Hz$ is between $1.7$ and $2.1M_{\sun}$. Central stellar density and
proton fraction decrease with increasing rotational frequency with respect to
static models, and depending on the exact stellar mass and angular velocity,
can drop below the Direct Urca threshold thus closing the fast cooling channel.
