  In this paper, we look at the following question. We consider cellular
automata in the hyperbolic plane and we consider the global function defined on
all possible configurations. Is the injectivity of this function undecidable?
The problem was answered positively in the case of the Euclidean plane by
Jarkko Kari, in 1994. In the present paper, we give a partial answer: when the
configurations are restricted to a certain condition, the problem is
undecidable.
