Boris Kruglikov and Marius Overholt.
"Pseudoholomorphic mappings and Kobayashi hyperbolicity".

  To appear in Differential Geometry and its Applications (1999).

We extend the definition of the Kobayashi pseudodistance to
almost complex manifolds. This pseudodistance is an invariant
of the geometry of pseudoholomorphic disks. Using Nijenhuis-Woolf
existence result and Gromov theory of pseudoholomorphic curves we extend
some complex theorems to the almost complex case. In connection
with the automorphism group we study the almost complex manifold
of pseudoholomorphic 1-jets of almost complex automorphisms.
We also get some criteria of entire complex lines existence.