Rigidity of proper holomorphic mappings between certain nonequidimensional unbounded non-hyperbolic domains

Abstract

The Fock-Bargmann-Hartogs domain Dn,m(μ)(μ>0) in Cn+m is defined by the inequality ‖w‖2<e−μ‖z‖2, where (z,w)∈Cn×Cm, which is an unbounded non-hyperbolic domain in Cn+m. In this article, we prove that any proper holomorphic mapping from Dn,m(μ) to Dn,m+1(μ)(m≥3) is necessarily the standard linear embedding up to their automorphisms and therefore is a totally geodesic isometric embedding with respect to their Bergman metrics.