ScholarWorks@경상국립대학교

초록

Let Bn be the unit ball in Cn and Hn be the homogeneous Siegel domain of the second kind which is biholomorphic to Bn . We show that the Kähler potential of Hn is unique up to the automorphisms among Kähler potentials whose differentials have constant norms. As an application, we consider a domain Ω in Cn , which is biholomorphic to Bn . We show that if Ω is affine homogeneous, then it is affine equivalent to Hn . Assume next that its canonical potential with respect to the Kähler–Einstein metric has a differential with a constant norm. If the biholomorphism between Ω and Bn is a restriction of a Möbius transformation, then the map is affine equivalent to a Cayley transform. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.