  The tensor-virial method is applied for a study of oscillation modes of
uniformly rotating Bose-Einstein condensed gases, whose rigid body rotation is
supported by an vortex array. The second order virial equations are derived in
the hydrodynamic regime for an arbitrary external harmonic trapping potential
assuming that the condensate is a superfluid at zero temperature. The
axisymmetric equilibrium shape of the condensate is determined as a function of
the deformation of the trap; its domain of stability is bounded by the
constraint $\Omega<1$ on the rotation rate (measured in units of the trap
frequency $\omega_0$.) The oscillations of the axisymmetric condensate are
stable with respect to the transverse-shear, toroidal and quasi-radial modes of
oscillations, corresponding to the $l= 2$, $| m| = 0,1,2 $ surface
deformations. In non-axisymmetric traps, the equilibrium constrains the
(dimensionless) deformation in the plane orthogonal to the rotation to the
domain $A_2 > \Omega^2$ with $\Omega< 1$. The second harmonic oscillation modes
in non-axisymmetric traps separate into two classes which have even or odd
parity with respect to the direction of the rotation axis. Numerical solutions
show that these modes are stable in the parameter domain where equilibrium
figures exist.
