In this paper some relation among the Dirac operator on a Riemannian spin-manifold $N$, its projection on some embedded hypersurface $M$ and the Dirac operator on $M$ with respect to the induced (called standard) spin structure are given.
@article{118583, author = {Jarol\'\i m Bure\v s}, title = {Dirac operators on hypersurfaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {313-322}, zbl = {0781.53031}, mrnumber = {1241739}, language = {en}, url = {http://dml.mathdoc.fr/item/118583} }
Bureš, Jarolím. Dirac operators on hypersurfaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 313-322. http://gdmltest.u-ga.fr/item/118583/
The Penrose Transform: its interaction with representation theory, Oxford Univ. Press, Oxford, 1989. | MR 1038279 | Zbl 0726.58004
Spin-Strukturen und Dirac-Operatoren über pseudo-riemannschen Mannigfaltigheiten, Leipzig, 1981.
Twistor and Killing spinors on Riemannian manifolds, Seminarbericht Nr.108, Berlin, Juli 1990. | MR 1084369 | Zbl 0705.53004
Clifford analysis, Research Notes in Math., 76, Pitman, 1982. | MR 0697564 | Zbl 1058.30043
Clifford Algebra and Spinor-Valued Functions, Math. and Its Applications, Kluwer, 1992. | MR 1169463
The Dirac operator, Mimeographed lecture notes MÚKU, 1991, .
Analysis on Lie groups and homogeneous spaces, Reg. conf. series in Math. 14 (1972), American Math. Society. | MR 0316632 | Zbl 0264.22010
Monogenic functions on surfaces, Journal Reine Angew. Math. 361 (1985), 145-181. (1985) | MR 0807257 | Zbl 0557.30042
Spin Geometry, Princeton University Press, Princeton, 1989. | MR 1031992 | Zbl 0688.57001