  This article investigates local properties of the further generalized
Weierstrass relations for a spin manifold $S$ immersed in a higher dimensional
spin manifold $M$ from viewpoint of study of submanifold quantum mechanics. We
show that kernel of a certain Dirac operator defined over $S$, which we call
submanifold Dirac operator, gives the data of the immersion. In the derivation,
the simple Frobenius reciprocity of Clifford algebras $S$ and $M$ plays
important roles.
