Light-Cone Parametrizations for KÄhler Manifolds

Abstract

It is shown that, for any Kähler manifold, there exist parametrizations such that the metric takes a block-form identical to the light-cone metric introduced by Polyakov for two-dimensional gravity. Besides its possible relevence for various aspects of Kählerian geometry, this fact allows us to change gauge in W gravities, and explicitly go from the conformal (Toda) gauge to the light-cone gauge using the W-geometry we proposed earlier (this will be discussed in detail in a forthcoming article).