Special properties of a submanifold of su(3)

The finite gauge transformation, in the submanifold of su(3) introduced in hep-th/9902027, is found to be linear in the gauge functions ${\omega}^a$'s. In this manner, a parameterization of SU(3) in terms of a single real octet vector ${\omega}^a$ is achieved. Under this finite transformation, those gauge fields satisfying $D^{ab}_{\mu}{\omega}^b = 0$, remain unchanged. A geometric meaning to the submanifold in terms of rotations in E8 is presented.