Generalized Weierstrass Relations and Frobenious Reciprocity

This article provides further generalized Weierstrass relations for a spin manifold S immersed in a higher dimensional spin manifold M ; we show that kernel of a certain Dirac operator defined over S, which we called submanifold Dirac operator, gives the data of the immersion. In the derivation, we use a relation between the generalized Weierstrass relations and the Frobenious reciprocity of Clifford algebras S and M .