Finite W3 transformations in a multi-time approach

Abstract Classical W 3 transformations are discussed as restricted diffeomorphism transformations ( W - Diff ) in two-dimensional space. We formulate them by using Riemannian geometry as a basic ingredient. The extended W 3 generators are given as particular combinations of Christoffel symbols. The defining equations of W - Diff are shown to depend on these generators explicitly. We also consider the issues of finite transformations, global SL(3) transformations and W - Schwarzians .