Mathematics – Differential Geometry
Scientific paper
2001-01-03
Mathematics
Differential Geometry
AMS-Tex Use 32 pages. to appear in Advanced Studies in Pure Mathematics
Scientific paper
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
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