Conformality in the sense of Gromov and holomorphy

M.Gromov extended the concepts of conformal and quasiconformal mapping to the mappings acting between the manifolds of different dimensions. For instance, any entire holomorphic function $ f: \Cn \to {\mathbb C}$ defines a mapping conformal in the sense of Gromov. In this connection Gromov addressed a natural question: which facts of the classical theory apply to these mappings? In particular is it true that {\em If the mapping $ F: \R^{n + 1} \to \R^{n}$ is conformal and bounded, then it is a constant mapping, provided that $ n \geq 2 $}~? We present arguments confirming the validity of such a Liouville-type theorem.