Isaev, Alexander2018-01-040022-247Xhttp://hdl.handle.net/1885/139055This note concerns tube domains in C² with the envelope of holomorphy not equal to the entire space. We construct examples showing that for such domains the sufficient condition for Kobayashi hyperbolicity due to M. Jarnicki and P. Pflug cannot be replaced by its weaker “affine” variant, which is known to be a necessary condition for hyperbolicity. Thus, we arrive at the somewhat unexpected conclusion that the obstructions for a domain in the above class to be Kobayashi hyperbolic are not just “affine”.application/pdf© 2017 Elsevier B.V.Kobayashi hyperbolicityTube domains in complex space2018-04-0110.1016/j.jmaa.2017.11.043