$W_{\infty}$--Geometry and Associated Continuous Toda System

Mikhail V. Saveliev; Svetlana A. Savelieva

doi:10.1016/0370-2693(93)91190-X

paper

$W_{\infty}$ --Geometry and Associated Continuous Toda System

arXiv:hep-th/9305152 · doi:10.1016/0370-2693(93)91190-X

Abstract

We discuss an infinite--dimensional kählerian manifold associated with the area--preserving diffeomorphisms on two--dimensional torus, and, correspondingly, with a continuous limit of the $A_{r}$ --Toda system. In particular, a continuous limit of the $A_{r}$ --Grassmannians and a related Plücker type formula are introduced as relevant notions for $W_{\infty}$ --geometry of the self--dual Einstein space with the rotational Killing vector.

6 pages, no figure report\# ETH-TH/93-21

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$W_{\infty}$ --Geometry and Associated Continuous Toda System