  We have performed hydrodynamic simulations of relativistic rotational
supernova core collapse in axisymmetry and have computed the gravitational
radiation emitted by such an event. Details of the methodology and of the
numerical code have been given in an accompanying paper. We have simulated the
evolution of 26 models in both Newtonian and relativistic gravity. Our
simulations show that the three different types of rotational supernova core
collapse and gravitational waveforms identified in previous Newtonian
simulations (regular collapse, multiple bounce collapse, and rapid collapse)
are also present in relativistic gravity. However, rotational core collapse
with multiple bounces is only possible in a much narrower parameter range in
relativistic gravity. The relativistic models cover almost the same range of
gravitational wave amplitudes and frequencies as the corresponding Newtonian
ones. For a given model, relativistic gravity can cause a large increase of the
characteristic signal frequency of up to a factor of five, which may have
important consequences for the signal detection. The gravitational wave signals
obtained in our study are within the sensitivity range of the first generation
laser interferometer detectors if the source is located within the Local Group.
