  Incompressible fields are of a special importance in electrodynamics, fluid
mechanics, and quantum mechanics. We shall derive a few expressions for such
fields in a Riemannian manifold, and show how to generate an incompressible
field from an arbitrary set of scalar differentiable functions. The concept of
compressibility removing factors of an arbitrary vector field is introduced and
utilized to obtain from an arbitrary vector field an incompressible one that
has the same vector surfaces as the original field. A general expression for
compressibility removing factors of a vector field is derived. The method is
applied to central fields.
