In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain Dn,m in C n ×C m which is defined by the inequality ζ 2 < e −µ z 2 .

Abstract. In this paper, the conjecture on the Zalcmanness of C n (n ≥ 2) and (C * ) 2 , which is posed in our previous work, is proved in the case where the derivatives of limit holomorphic curves are bounded. Moreover, several criteria for normality of families of holomorphic mappings are given.

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