Weierstrass Relation for a Submanifold $S^k$ in $\EE^n$ Coming from Submanifold Dirac Operator
Differential Geometry
2007-05-23 v4 Mathematical Physics
math.MP
Abstract
Using the submanifold quantum mechanical scheme, the restricted Dirac operator in a submanifold is defined. Then it is shown that the zero mode of the Dirac operator expresses the local properties of the submanifold, such as the Frenet-Serret and generalized Weierstrass relations. In other words this article gives a representation of a further generalized Weierstrass relations for a general k-spin manifolds immersed in n-dimensional euclidean space (0<k<n).
Keywords
Cite
@article{arxiv.math/0101020,
title = {Weierstrass Relation for a Submanifold $S^k$ in $\EE^n$ Coming from Submanifold Dirac Operator},
author = {Shigeki Matsutani},
journal= {arXiv preprint arXiv:math/0101020},
year = {2007}
}
Comments
AMS-Tex Use 32 pages. to appear in Advanced Studies in Pure Mathematics