  Recently discovered quasi periodic oscillations in the X-ray brightness of
low mass X-ray binaries are used to derive constraints on the mass of the
neutron star component and the equation of state of neutron star matter. The
observations are compared with models of rapidly rotating neutron stars which
are calculated by means of an exact numerical method in full relativity. For
the equations of state we select a broad collection of models representing
different assumptions about the many-body structure and the complexity of the
composition of super dense matter. The mass constraints differ from their
values in the approximate treatment by \sim 10%. Under the assumption that the
maximum frequency of the quasi periodic oscillations originates from the
innermost stable orbit the mass of the neutron star is in the range: $M\sim
1.92-2.25 M_\odot$. Especially the quasi periodic oscillation in the
Atoll-source 4U 1820-30 is only consistent with equations of state which are
rather stiff at high densities which is explainable, so far, only with pure
nucleonic/leptonic composition. This interpretation contradicts the hypothesis
that the protoneutron star formed in SN 1987A collapsed to a black hole, since
this would demand a maximum neutron star mass below $1.6 M_\odot$. The recently
suggested identification of quasi periodic oscillations with frequencies around
10 Hz with the Lense-Thirring precession of the accretion disk is found to be
inconsistent with the models studied in this work, unless it is assumed that
the first overtone of the precession is observed.
