  In one complex variable, the cross ratio is a well-known quantity associated
with four given points in the complex plane that remains invariant under linear
fractional maps. In particular, if one knows where three points in the complex
plane are mapped under a linear fractional map, one can use this invariance to
explicitly determine the map and to show that linear fractional maps are
$3$-transitive. In this paper, we define a generalized cross ratio and
determine some of its basic properties. In particular, we determine which
hypotheses must be made to guarantee that our generalized cross ratio is well
defined. We thus obtain a class of maps that obey similar transitivity
properties as in one complex dimension, under some more restrictive conditions.
