Pin Structures and the Dirac Operator on Real Projective Spaces and Quadrics

  • Michel Cahen
  • Simone Gutt
  • Andrzej Trautman
Part of the Fundamental Theories of Physics book series (FTPH, volume 94)


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.

Key words

Dirac operator pin structures real projective spaces real projective quadrics 


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  1. Baum, H., Friedrich, Th., Grunewald, R. and Kath, I.: 1991, Twistors and Killing spinors on Riemannian manifolds, Teubner-Verlag, Leipzig-Stuttgart.zbMATHGoogle Scholar
  2. 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.MathSciNetzbMATHGoogle Scholar
  3. Cahen, M., Gutt, S., Lemaire, L. and Spindel, T.: 1986, ‘Killing spinors’, Bull. Soc. Math. Belg. Sér. A Vol. no. 38, pp. 75–102.MathSciNetzbMATHGoogle Scholar
  4. Cahen, M., Gutt, S. and Trautman, A.: 1993, ‘Spin structures on real projective quadrics’, J. Geom. Phys., Vol. no. 10, pp. 127–154.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Cahen, M., Gutt, S. and Trautman, A.: 1995, ‘Pin structures and the modified Dirac operator’, J. Geom. Phys., Vol. no. 17, pp. 283–297.MathSciNetzbMATHCrossRefGoogle Scholar
  6. Dćbrowski, L. and Trautman, A.: 1986, ‘Spin structures on spheres and projective spaces’, J. Math. Phys. Vol. no. 27, pp. 2022–2028.MathSciNetCrossRefGoogle Scholar
  7. Friedrich, Th.: 1980, ‘Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung’, Math. Nachr. Vol. no. 97, pp. 117–146.MathSciNetzbMATHCrossRefGoogle Scholar
  8. Hitchin, N.: 1974, ‘Harmonic spinors’, Adv. Math. Vol. no. 14, pp. 1–55.MathSciNetzbMATHCrossRefGoogle Scholar
  9. Lichnerowicz, A.: 1963, ‘Spineurs harmoniques’, C. R. Acad. Sci. Paris Sér. A-B Vol. no. 257, pp. 7–9.MathSciNetzbMATHGoogle Scholar
  10. Trautman, A.: 1995, ‘The Dirac operator on hyp ersurfaces’, Acta Phys. Polon. B Vol. no. 7, pp. 1283–1310.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Michel Cahen
    • 1
  • Simone Gutt
    • 1
  • Andrzej Trautman
    • 2
  1. 1.Département de MathématiquesUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Instytut Fizyki TeoretycznejUniwersytet WarszawskiWarszawaPoland

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