CP symmetry and fermion masses in O(10) grand unification models

O(10) grand unification models which do not necessarily have an extra global symmetry are discussed, taking the model with one 10-plet in the Yukawa sector as an example. A strong correlation between mass ratios and CP is found. The mass relation $m_t/m_b=v_u/v_d$ is recovered when $G_W=0$; and another special relation $m_t/m_b=G_E/G_W$ appears when $v_d=0$, where $G_{E,W}$ are Yukawa coupling constants and $v_{u,d}$ are VEVs. To facilitate this discussion, a set of $O(10)$ $\gamma$- matrices is offered based on a physical representation of the spinors and that of the vector of the $SO(10)$ group. Flavor changing neutral currents in such models are also discussed.