ANDREA LOI
Holomorphic maps of Hartogs domains into complex space forms
Pages: 103-113
Received: 21 May 2002
Revised: 24 September 2002
Mathematics Subject Classification (2000): 53C55 - 53C25
Abstract: Let HF be a Hartogs domain with strictly pseudoconvex boundary endowed with its natural Kähler metric gF (see Sect. 2). Following Calabi [1] we give necessary and sufficient conditions for (HF, gF) to admit a holomorphic and isometric map into a finite or infinite dimensional complex space form. Moreover we prove that, if gF is Einstein, then (HF, gF) is biholomorphically isometric to the unit ball endowed with the hyperbolic metric.