  The influence of a uniform rotation with frequency Omega on the critical
behavior of liquid 4He near T_lambda is investigated. We apply our recently
developed approach which is a renormalization-group theory based on model F
starting with the calculation of the Green's function in Hartree approximation.
We calculate the specific heat, the correlation length, and the thermal
resistivity tensor as functions of the temperature T for fixed values of the
rotation frequency Omega. For nonzero Omega we find that all physical
quantities are smooth near T_lambda so that the superfluid transition is a
smooth crossover. We define a frequency-dependent transition temperature
T_lambda(Omega) by the maximum of the specific heat and present a power law
prediction. For T<T_lambda(Omega) we find mutual friction between the
superfluid and the normal-fluid component caused implicitly by the motion of
vortex lines and calculate the Vinen coefficients B and B'.
