The $SU_3$ Space and Its Quotient Spaces

A metric description of symmetric Riemannian spaces is needed for constructing gauge fields with a symmetry. We describe the group $SU_3$ as a Riemannian space for two different parameterizations and develop a Hamiltonian technique for constructing quotient spaces. We construct the quotient spaces of the group $SU_3$, namely, the six-dimensional quotient space $(SU_3/O_2^2)$, the five-dimensional quotient space $(SU_3/O_3)$, and the two four-dimensional quotient spaces $(SU_3/O_2^4)$ and $(SU_3/O_3/O_2)$.