Uniqueness of Kahler-Ricci solitons on compact Kahler manifolds

We introduce a new holomorphic invariant on any compact Kahler manifolds with positive first Chern class and nontrivial holomorphic vector fields, which contains the Futaki invariant as a special case. This invariant is shown to be an obstruction to the existence of Kahler-Ricci solitons. By solving a complex Monge-Ampere equation, we prove the uniqueness of Kahler-Ricci solitons. (C) 1999 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000084722800011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701MathematicsSCI(E)5ARTICLE11991-99532