Abstract
This is a brief summary of our work on an explicit description of (s)pin structures of real projective quadrics and on the spectrum of the Dirac operator on these spaces.
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References
Baum, H., Friedrich, Th., Grunewald, R. and Kath, I.: 1991, Twistors and Killing spinors on Riemannian manifolds, Teubner-Verlag, Leipzig-Stuttgart.
Cahen, M. and Gutt, S.: 1988, ‘Spin structures on compact simply connected Riemannian symmetric spaces’, Simon Stevin Quart. J. Pure Appl. Math. Vol. no. 62, pp. 209–242.
Cahen, M., Gutt, S., Lemaire, L. and Spindel, T.: 1986, ‘Killing spinors’, Bull. Soc. Math. Belg. Sér. A Vol. no. 38, pp. 75–102.
Cahen, M., Gutt, S. and Trautman, A.: 1993, ‘Spin structures on real projective quadrics’, J. Geom. Phys., Vol. no. 10, pp. 127–154.
Cahen, M., Gutt, S. and Trautman, A.: 1995, ‘Pin structures and the modified Dirac operator’, J. Geom. Phys., Vol. no. 17, pp. 283–297.
Dćbrowski, L. and Trautman, A.: 1986, ‘Spin structures on spheres and projective spaces’, J. Math. Phys. Vol. no. 27, pp. 2022–2028.
Friedrich, Th.: 1980, ‘Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung’, Math. Nachr. Vol. no. 97, pp. 117–146.
Hitchin, N.: 1974, ‘Harmonic spinors’, Adv. Math. Vol. no. 14, pp. 1–55.
Lichnerowicz, A.: 1963, ‘Spineurs harmoniques’, C. R. Acad. Sci. Paris Sér. A-B Vol. no. 257, pp. 7–9.
Trautman, A.: 1995, ‘The Dirac operator on hyp ersurfaces’, Acta Phys. Polon. B Vol. no. 7, pp. 1283–1310.
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Cahen, M., Gutt, S., Trautman, A. (1998). Pin Structures and the Dirac Operator on Real Projective Spaces and Quadrics. In: Dietrich, V., Habetha, K., Jank, G. (eds) Clifford Algebras and Their Application in Mathematical Physics. Fundamental Theories of Physics, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5036-1_30
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DOI: https://doi.org/10.1007/978-94-011-5036-1_30
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