The above conclusion is demonstrated in the light of poincare theorem, it is demonstrated by using contraction (interior product) of vector field and differential form as well as operation of exterior differentiation.

By estimating the koppelman kernel on Complex Manifolds, the difference between the koppelman kernel on complex manifolds and the Bochner Martinelli koppelman on C n was obtained;and then by utilizing the koppelman formula and the result as above, the jump formula of differential forms under Berndtsson transform on Complex manifolds was derived.

By the natural and harmonious relationship between differential forms and differential equations and between differential forms and vector analysis, we discuss the properties, which are covariant under the transformation of coordinates in the framework of differential forms, of particle motion in a central force field.

The Hypo-elliptic Differential Forms on Smooth Manifolds;

Let X be a smooth oriented Riemannian n-manifold without boundary,l-form W be WT2 class of differential forms on X.

The exterior differential form was pointed out to be the mathematical model of a lot of proposition in field theory.

Thenecessity and urgency were discussed that exterior differential form and some content of mordenmathematics were introduced in teaching.

This paper introduces the concept of Finslerian exterior differential form and two exterior differential operators dh,dv,which are different from the general theory of Cartan s.