Spinors and the Dirac operator on hypersurfaces. I. General theory
Copyright policy )Spinors and the Dirac operator on hypersurfaces. I. General theory
It is shown that a hypersurface immersed isometrically into the Euclidean space Rn+1, where n=2ν or 2ν+1, has a pin structure such that the associated bundle of 2ν-component spinors is trivial. This is used to derive a new formula for the Dirac operator on hypersurfaces. The Dirac operator is slightly modified to be compatible with the twisted adjoint representation of the pin group. When Rn+1 is foliated by hypersurfaces, then the Dirac operator in Rn+1 splits into a radial and a tangential part with respect to the foliation. There is a corresponding new formula for the Laplacian.
pin structure, Elliptic equations on manifolds, general theory, Dirac operator, Spin and Spin\({}^c\) geometry, hypersurfaces in Euclidean space, Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism, spinors
pin structure, Elliptic equations on manifolds, general theory, Dirac operator, Spin and Spin\({}^c\) geometry, hypersurfaces in Euclidean space, Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism, spinors
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