  A unimodular complex surface is a complex 2-manifold X endowed with a
holomorphic volume form. A strictly pseudoconvex real hypersurface M in X
inherits not only a CR-structure but a canonical coframing as well.
  In this article, this canonical coframing on M is defined, its invariants are
discussed and interpreted geometrically, and its basic properties are studied.
  A natural evolution equation for strictly pseudoconvex real hypersurfaces in
unimodular complex surfaces is defined, some of its properties are discussed,
and several examples are computed.
  The locally homogeneous examples are determined and used to illustrate
various features of the geometry of the induced structure on the hypersurface.
