  In this article we give a classification of three dimensional m-quasi
Einstein manifolds with two distinct Ricci-eigen values. Our study provides
explicit description of local and complete metrics and potential functions. We
also describe the associated warped product Einstein manifolds in detail. For
the proof we present a Codazzi tensor on any three dimensional $m$-quasi
Einstein manifold and use geometric properties of the tensor which help to
analyze the m-quasi Einstein equation effectively. A technical advance over
preceding studies is made by resolving the case when the gradient $\nabla f$ of
the potential function is not a Ricci-eigen vector field.
