  The adiabatic geometric phases for general three state systems are discussed.
An explicit parameterization for space of states of these systems is given. The
abelian and non-abelian connection one-forms or vector potentials that would
appear in a three dimensional quantum system with adiabatic characteristics are
given explicitly. This is done in terms of the Euler angle parameterization of
SU(3) which enables a straight-forward calculation of these quantities and its
immediate generalization.
