References
Atiyah, M. F.; Hitchin, N.: The Geometry and Dynamics of Magnetic Monopoles. Princeton University Press 1988.
Baum, H.: Spin-Strukturen und Dirac-Operatoren über pseudo-Riemannschen Mannigfaltigkeiten. Teubner-Texte zur Mathematik Bd.41, Teubner-Verlag, Leipzig 1981.
Besse, A. L.: Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, Band10, Springer-Verlag 1987.
Cahen, M.; Gutt, S.; Lemaire, L.; Spindel, P.: Killing Spinors. Bulletin de la Société Mathématique de Belgique, t. XXXVIIIA, 1986, 75–102.
Duff, M. J.; Nilsson, B.; Pope, C. N.: Kaluza-Klein Supergravity. Phys. Rep.130 (1986), 1–142.
Eguchi, T.; Gilkey, P. B.; Hanson, A. J.: Gravitation, Gange theories and Differential Geometry. Physics Reports 66, No. 6 (1980).
Franc, A.: Spin-Structures and Killing spinors on Lens spaces. Preprint.
Friedrich, Th.: Der erste Eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung. Math. Nachr.97 (1980), 117–146.
Friedrich, Th.: Zur Existenz paralleler Spinorfelder über Riemannschen Mannigfaltigkeiten. Colloquium mathematicum, Vol. XLIV, Fasc.2 (1981), 277–290.
Friedrich, Th.: A remark on the first eigenvalue of the Dirac operator on 4-dimensional manifolds. Math. Nachrichten102 (1981), 53–56.
Friedrich, Th.: On the conformal relation between twistors and Killing spinors, to appear.
Friedrich, Th.; Grunewald, R.: On the first eigenvalue of the Dirac operator on 6-dimensional manifolds. Ann. of Global Analysis and Geometry3 (1985) 3, 265–273.
Friedrich, Th.; Kath, I.: Einstein manifolds of dimension five with small first eigenvalue of the Dirac operator. To appear in Journal of Differential Geometry.
Friedrich, Th.; Kath, I.: Compact 5-dimensional Riemannian manifolds with parallel spinors. To appear in Math. Nachrichten.
Friedrich, Th.; Kath, I.: Compact seven-dimensional manifolds with Killing spinors. To appear.
Gibbons, G.W.; Hawking, S. W.: Gravitational multiinstantons. Phys. Lett. B78 (1978), 430–432.
Grunewald, R.: Untersuchungen über Einstein-Metriken auf 6-dimensionalen Mannigfaltigkeiten. Diss. A, 1987. Berlin, Humboldt-Universität, Sektion Mathematik.
Hijazi, O.: Caractérisation de la sphère par les premières valeurs propres de l'opérateur de Dirac en dimensions 3, 4, 7 et 8. C.R. Acad. Sci. Paris, Ser. I303 (1986) 9, 417–419.
Hijazi, O.: A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors. Comm. Math. Physics104 (1986) 1, 151–162.
Hitchin, N.: Compact four-dimensional Einstein manifolds, Journ. of Diff. Geometry9 (1974), 435–441.
Hitchin, N.: Polygons and gravitations. Math. Proc. Cambr. Phil. Soc. (1979) 85, 465–476.
Kronheimer, P. B.: The construction of gravitational instantons as hyperkähler quotients. Preprint.
Nilsson, B. C.; Pope, C. N.: Scalar and Dirac eigenfunctions on the squashed seven-sphere. Phys. Lett. B.133 (1983) 1/2, 67–71.
Sulanke, S.: Der erste Eigenwert des Dirac operators aufS 5 /T. Math. Nachr.99 (1980), 259–271.
Wolf, J. A.: Spaces of constant curvature. Berkeley, Calif., 1972:
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baum, H. Odd-dimensional Riemannian manifolds with imaginary Killing spinors. Ann Glob Anal Geom 7, 141–153 (1989). https://doi.org/10.1007/BF00127864
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00127864