Submanifold Differential Operators in $\Cal D$-Module Theory II: Generalized Weierstrass and Frenet-Serret Relations as Dirac Equations
| dc.creator | Matsutani, Shigeki | |
| dc.date | 1999-10-09 | |
| dc.date | 2000-01-09 | |
| dc.date.accessioned | 2026-07-07T05:31:07Z | |
| dc.date.available | 2026-07-07T05:31:07Z | |
| dc.description | 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. | |
| dc.description | AMS-Tex Use 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/9910052 | |
| dc.identifier | http://arxiv.org/abs/math/9910052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79226 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.title | Submanifold Differential Operators in $\Cal D$-Module Theory II: Generalized Weierstrass and Frenet-Serret Relations as Dirac Equations | |
| dc.type | text |