Generalized Weierstrass Relations and Frobenius reciprocity

Abstract

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.

17pages. to be published in Mathematical Physics, Analysis and Geometry

References in corpus (5)

• On the Spinor Representation of Surfaces in Euclidean 3-Space
• Generalized Weierstrass representation for surfaces in multidimensional Riemann spaces
• Surfaces in the four-space and the Davey--Stewartson equations
• Immersion Anomaly of Dirac Operator on Surface in R^3
• Electron wave functions on $T^2$ in a static magnetic field of arbitrary direction

Cited by in corpus (1)

• Gauss Optics and Gauss Sum on an Optical Phenomena