  Cranked Relativistic Hartree-Bogoliubov theory without and with approximate
particle number projection by means of the Lipkin-Nogami method is presented in
detail as an extension of Relativistic Mean Field theory with pairing
correlations to the rotating frame. Pairing correlations are taken into account
by a finite range two-body force of Gogny type. The applicability of this
theory to the description of rotating nuclei is studied in detail on the
example of superdeformed bands in even-even nuclei of the $A\sim 190$ mass
region. Different aspects such as the importance of pairing and particle number
projection, the dependence of the results on the parametrization of the RMF
Lagrangian and Gogny force etc. are investigated in detail. It is shown that
without any adjustment of new parameters the best description of experimental
data is obtained by using the well established parameter sets NL1 for the
Lagrangian and D1S for the pairing force. Contrary to previous studies at spin
zero it is found that the increase of the strength of the Gogny force is not
necessary in the framework of Relativistic Hartree-Bogoliubov theory provided
that particle number projection is performed.
