  In this paper, a generalization of the "sector property" theorem first
pioneered by Baouendi, Rothschild and Treves is given. The main contribution
consists in showing that if a submanifold of $\C^n$ with higher codimension is
locally presented in a weighted normal form, similar to that described by Bloom
and Graham, then a characterization is given as to when a vector in the tangent
space belongs to the analytic wave front set for the set of locally defined CR
functions on the submanifold. This characterization is described in terms of
the sign of the inner product of this vector with the local graphing functions
for the submanifold on sectors of suitable size along complex lines in its
tangent space. Examples are given to show that under certain circumstances, the
results are sharp. Previous results by Baouendi et. al. contained a
semi-rigidity assumption which is not assumed in the present paper. The
hypoanalytic wave front set determines the cone of directions in which CR
functions extend analytically to the ambient space and thus provides an
explicit description of the local hull of holomorphy of a submanifold of
$\C^n$.
