ON PROPER HOLOMORPHIC MAPPINGS BETWEEN TWO EQUIDIMENSIONAL FBH-TYPE DOMAINS
- 1 January 2020
- journal article
- research article
- Published by Faculty of Mathematics, Kyushu University in Kyushu Journal of Mathematics
- Vol. 74 (1), 149-167
- https://doi.org/10.2206/kyushujm.74.149
Abstract
We introduce a new class of domains Dn,m(μ, p), called FBH-type domains, in ℂn × ℂm, where 0 < μ ∈ ℝ and p ∈ ℕ. In the special case of p = 1, these domains are just the Fock-Bargmann-Hartogs domains Dn,m(μ) in ℂn × ℂm introduced by Yamamori. In this paper we obtain a complete description of an arbitrarily given proper holomorphic mapping between two equidimensional FBH-type domains. In particular, we prove that the holomorphic automorphism group Aut(Dn,m(μ, p)) of any FBH-type domain Dn,m(μ, p) with p ≠ 1 is a Lie group isomorphic to the compact connected Lie group U(n) × U(m). This tells us that the structure of Aut(Dn,m(μ, p)) with p ≠ 1 is essentially different from that of Aut(Dn,m(μ)).Keywords
This publication has 8 references indexed in Scilit:
- A localization principle for biholomorphic mappings between the Fock-Bargmann-Hartogs domainsHiroshima Mathematical Journal, 2018
- Rigidity of proper holomorphic mappings between certain unbounded non-hyperbolic domainsJournal of Mathematical Analysis and Applications, 2014
- The automorphism group of a certain unbounded non-hyperbolic domainJournal of Mathematical Analysis and Applications, 2014
- Proper holomorphic mappings, Bell’s formula, and the Lu Qi-Keng problem on the tetrablockArchiv der Mathematik, 2013
- On the holomorphic automorphism group of a generalized complex ellipsoidComplex Variables and Elliptic Equations, 2013
- The Bergman kernel of the Fock–Bargmann–Hartogs domain and the polylogarithm functionComplex Variables and Elliptic Equations, 2013
- Pseudohermitian invariants and classification of CR mappings in generalized ellipsoidsJournal of the Mathematical Society of Japan, 2012
- THE REPRESENTATIVE DOMAIN OF A HOMOGENEOUS BOUNDED DOMAINKyushu Journal of Mathematics, 2009