Invariant metrics and Laplacians on Siegel-Jacobi disk

Abstract

Let Dn be the generalized unit disk of degree n. In this paper, Riemannian metrics on the Siegel-Jacobi disk Dn × C(m,n) which are invariant under the natural action of the Jacobi group are found explicitly and the Laplacians of these invariant metrics are computed explicitly. These are expressed in terms of the trace form. © 2009 Editorial Office of CAM (Fudan University) and Springer Berlin Heidelberg.