  This article is one of a series of papers. For this decade, the Dirac
operator on a submanifold has been studied as a restriction of the Dirac
operator in $n$-dimensional euclidean space $\EE^n$ to a surface or a space
curve as physical models. These Dirac operators are identified with operators
of the Frenet-Serret relation for a space curve case and of the generalized
Weierstrass relation for a conformal surface case and completely represent the
submanifolds. For example, the analytic index of Dirac operator of a space
curve is identified with its writhing number. As another example, the operator
determinants of the Dirac operators are closely related to invariances of the
immersed objects, such as Euler-Bernoulli and Willmore functionals for a space
curve and a conformal surface respectively. In this article, we will give
mathematical construction of the Dirac operator by means of $\Cal D$-module and
reformulate my recent results mathematically.
