On the Kobayashi hyperbolicity of certain tube domains

Abstract:

In an article from 2008 the second author introduced three families of tube domains in $\mathbb {C}^2$ with holomorphic automorphism group isomorphic to $\mathbb {R}\ltimes \mathbb {R}^2$ and envelope of holomorphy equal to $\mathbb {C}^2$. In the present paper we show that every domain in each of these families is Kobayashi-hyperbolic.