| Abstrakt: |
Abstract: We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain $D_{n,m}^p(\mu)$. The generalized Fock-Bargmann-Hartogs domain is defined by inequality ${\rm e}^{\mu\|z\|^2}\sum_{j=1}^m|\omega_j|^{2p}<1$, where $(z,\omega)\in\mathbb{C}^n\times\mathbb{C}^m$. In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic self-mapping of the generalized Fock-Bargmann-Hartogs domain $D_{n,m}^p(\mu)$ becomes a holomorphic automorphism if and only if it keeps the function $\botsmash{\sum_{j=1}^m}|\omega_j|^{2p}{\rm e}^{\mu\|z\|^2}$ invariant. |
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