Vanishing theorems and eigenvalue estimates in Riemannian spin geometry

International Journal of Mathematics

Volumn 8, Issue 7, 1997, Pages 921-934

  Branson, Thomas ^a   Hijazi, Oussama ^b,c  

^a UNIVERSITY OF IOWA   (United States)

^b UNIVERSITÉ DE NANTES   (France)

^c UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944449516     PISSN: 0129167X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129167X97000433     Document Type: Article

References (22)

1. T. Aubin, Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. Pures Appl. 55 (1976), 269-296.
2. G. Bär, Lower eigenvalue estimates for Dirac operators, Math. Ann. 293 (1991), 39-46.
3. H. Baum, T. Friedrich, R. Grunewald and I. Kath, Twistor and Killing Spinors on Riemannian Manifolds, Seminarbericht vol. 108, Humboldt-Universität zu Berlin, 1990.
4. C. Bennett and T. Branson, Curvature actions, in preparation.
5. J.-P. Bourguignon, Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein, Invent. Math. 63 (1981), 263-286.
6. T. Branson, Conformally covariant equations on differential forms, Comm. Partial Differential Equations 7 (1982), 393-431.
7. T. Branson, Nonlinear phenomena in the spectral theory of geometric linear differential operators, Proc. Symp. Pure Math. 59 (1996), 27-65.
8. T. Branson, Stein-Weiss operators and ellipticity, J. Funct. Anal., to appear.
9. T. Branson, Second order conformal covariants, Proc. Amer. Math. Soc., to appear.
10. R. Brauer, Sur la multiplication des caractéristiques des groupes continus et semisimples, C.R. Acad. Sci. Paris 204 (1937), 1784-1786.
11. H. Fegan, Conformally invariant first order differential operators, Quart. J. Math. Oxford 27 (1976), 371-378.
12. S. Goldberg, Curvature and Homology, Dover Pub., New York, 1982.
13. O. Hijazi, A conformal lower bound on the smallest eigenvalue of the Dirac operator and Killing spinors, Commun. Math. Phys. 104 (1986), 151-162.
14. O. Hijazi, Première valeur propre de l'opérateur de Dirac et nombre de Yamabe, C.R. Acad. Sci. Paris 313 (1991), 865-868.
15. O. Hijazi and A. Lichnerowicz, Spineurs harmoniques, spineurs-twisteurs et géométrie conforme, C.R. Acad. Sci. Paris 307 (1988), 833-838.
16. J. Kazdan and F. Warner, Scalar curvature and conformal deformation of Riemannian structures, J. Diff. Geom. 10 (1975), 113-134.
17. M. Labbi, Sur les nombres de Betti des variétés conformément plates, C.R. Acad. Sci. Paris 319 (1994), 77-80.
18. J. Lafontaine, Remarques sur les variétés conformément plates, Math. Ann. 259 (1982), 313-319.
19. R. Penrose, Structure of space-time, Battelle Recontres, eds. C. DeWitt and J. Wheeler, Benjamin, New York, 1968.
20. E. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163-196.
21. R. Strichartz, Linear algebra of curvature tensors and their covariant derivatives, Canad. J. Math. 40 (1988), 1105-1143.
22. V. Wünsch, On conformally invariant differential operators, Math. Nachr. 129 (1986), 269-281.