Let D n be the generalized unit disk of degree n.In this paper,Riemannian metrics on the Siegel-Jacobi disk D n × C (m,n) which are invariant under the natural action of the Jacobi group are found explicitly and ...Let D n be the generalized unit disk of degree n.In this paper,Riemannian metrics on the Siegel-Jacobi disk D n × 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.展开更多
In this paper,we get the full expansion for period map from the moduli space Mg of curves to the coarse moduli space Ag of g-dimensional principally polarized abelian varieties in Bers coordinates.This generalizes ful...In this paper,we get the full expansion for period map from the moduli space Mg of curves to the coarse moduli space Ag of g-dimensional principally polarized abelian varieties in Bers coordinates.This generalizes fully the famous Rauch's variational formula.As applications,we compute the curvature of Siegel metric at point [X] with Π([X]) =√ -1 Ig and the Christoffel symbols of L2-induced Bergman metric on Mg.展开更多
基金supported by the Inha University Research Grant (No. 39628-1)
文摘Let D n be the generalized unit disk of degree n.In this paper,Riemannian metrics on the Siegel-Jacobi disk D n × 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.
文摘In this paper,we get the full expansion for period map from the moduli space Mg of curves to the coarse moduli space Ag of g-dimensional principally polarized abelian varieties in Bers coordinates.This generalizes fully the famous Rauch's variational formula.As applications,we compute the curvature of Siegel metric at point [X] with Π([X]) =√ -1 Ig and the Christoffel symbols of L2-induced Bergman metric on Mg.
