Finite W_3 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.

10 pages, UB-ECM-PF 94/20, TOHO-FP-9448, QMW-PH-94-25