  A coordinate-free definition for Wick-type symbols is given for symplectic
manifolds by means of the Fedosov procedure. The main ingredient of this
approach is a bilinear symmetric form defined on the complexified tangent
bundle of the symplectic manifold and subject to some set of algebraic and
differential conditions. It is precisely the structure which describes a
deviation of the Wick-type star-product from the Weyl one in the first order in
the deformation parameter. The geometry of the symplectic manifolds equipped by
such a bilinear form is explored and a certain analogue of the
Newlander-Nirenberg theorem is presented. The 2-form is explicitly identified
which cohomological class coincides with the Fedosov class of the Wick-type
star-product. For the particular case of K\"ahler manifold this class is shown
to be proportional to the Chern class of a complex manifold. We also show that
the symbol construction admits canonical superextension, which can be thought
of as the Wick-type deformation of the exterior algebra of differential forms
on the base (even) manifold. Possible applications of the deformed superalgebra
to the noncommutative field theory and strings are discussed.
