Gauge anomaly with vector and axial-vector fields in six dimensional curved space

Imposing the conservation equation of the vector current for a fermion of spin $\frac{1}{2}$ in quantum level, a gauge anomaly for the fermion coupling with nonabelian vector and axial--vector fields in six--dimensional curved space is expressed in tensorial form. The anomaly consists of terms which resemble the chiral U(1) anomaly and the commutator terms which disappear if the axial--vector field is abelian.