Abstract
Introduction of a first order operator D on the spinors, in terms of the Dirac operator; D is connected with the equation of the global twistors and conformally covariant. For a compact spin manifold of dimension n ≥ 3, the operator (∆-ρ) on the spinors (ρ = (n/4(n-1)R) is positive; Hijazi inequality holds for any spinor Ψ such that (PΨ, PΨ) =λ(Ψ,Ψ) with λ = const. In the limiting case, the manifold admits a Killing spinor.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Cremmer, B. Julia, J. Scherek, Phys . Lett 76 B, p. 409 (1978).
M. J. Duff, C.N. Pope in Supergravity 81 (Ed. S. Ferrara, J.G. Taylor) Cambridge Univ. Press London 1982.
L.P. Hughston, R. Penrose, P. Sommers, M. Walker, Comm. Math. Phys. 27, P.303 (1982).
B. Biran, F. Englert, B. de Wit, H. Nicolai, Phys. Lett. 124 B, p. 45 (1983).
P. Candelas, G. T. Horowitz, A. Strominger, E. Witten, Nucl. Phys. B 258, p.46 (1985).
A. Lichnerowicz, C.R. Acad. Sci. Paris A-B, 257, p.7 (1963).
T. Friedrich, Math. Nach 97, p.117 (1980).
O. Hijazi, A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors. Comm. Math. Phys. 104, 151, (1986).
M. Cahen, S. Gutt, L. Lemaire, P. Spindel, Killing spinors, Bull. Soc. Math. Belg. 38 A (1986) (to appear).
J.L. Kazdan, F.W. Warner, J. of Diff. Geom. 10, p.113 (1975).
T. Aubin, The scalar curvature in Differential Geometry and Relattvity (Ed. M. Cahen and M. Flato) Reidel Dordrecht p.5–18 (1976).
A. Lichnerowicz, C.R. Acad. Sci. Paris 303, série I, p. 811 (1986)
and Variétés spinorielles et universalité de l’inégalité de Hijazi, A. Lichnerowicz, C. R. Acad. Sci. Paris 304, série I, p.227 (1987).
H. Baum, Spin Struktures, p.138 Teubner, Leipzig (1981).
T. Branson and Y. Kossmann-Schwarzbach, Lett. Math. Phys. 7, p.138, (1983).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Lichenrowicz, A. (1988). Killing Spinors and Universality of the Hijazi Inequality. In: Bleuler, K., Werner, M. (eds) Differential Geometrical Methods in Theoretical Physics. NATO ASI Series, vol 250. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7809-7_17
Download citation
DOI: https://doi.org/10.1007/978-94-015-7809-7_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8459-0
Online ISBN: 978-94-015-7809-7
eBook Packages: Springer Book Archive