  Stark hypersurfaces are a special class of austere hypersurface in ${\mathbb
C}P^n$ where the shape operator is compatible with the $CR$-structure. In this
paper, the possible shape operators for stark hypersurfaces are completely
determined, and stark hypersurfaces in ${\mathbb C}P^2$ are constructed as
integrals of a Frobenius exterior differential system.
