References
Atiyah, M.F., Bott, R., Shapiro, A.: Clifford modules. Topology3 (Suppl. 1), 3–38 (1964)
Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four-dimensional Riemannian geometry. Proc. Soc. London A362, 425–461 (1978)
Besse, A.L.: Einstein manifolds. Berlin Heidelberg New York: Springer 1987
Friedrich, T.: Der erste Eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nicht negativer Skalarkrümmung. Math. Nachr.97, 117–146 (1980)
Friedrich, T., Kurke, H.: Compact four-dimensional self-dual Einstein manifolds with positive scalar curvature. Math. Nachr.106, 271–299 (1982)
Grunewald, R.: Untersuchungen über Einstein-Metriken auf 6-dimensionalen Mannigfaltigkeiten. Diss. A, Humboldt-Universität zu Berlin (1986)
Hermann, R.: On the Differential Geometry of foliations. Ann. Math.72, 445–457 (1960)
Hijazi, O.: A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors. Commun. Math. Phys.104, 151–162 (1986)
Hitchin, N.: Harmonic spinors. Adv. Math.14, 1–55 (1974)
Hitchin, N.: Kählerian twistor spaces. Proc. London Math. Soc. (3)43, 133–150 (1981)
Kirchberg, K.-D.: An estimation for the first eigenvalue of the Dirac operator on closed Kähler manifolds of positive scalar curvature. Ann. Glob. Anal. Geom.4 (No. 3) 291–325 (1986)
Kobayashi, S.: On compact Kähler manifolds with positive Ricci tensor. Ann. Math.74, 570–574 (1961)
Kobayashi, S.: Transformation groups in differential geometry. Berlin Heidelberg New York: Springer 1972
Kobayashi, S., Nomizu, K.: Foundations of differential geometry. I, II. New York: Wiley 1963, 1969
Lascaux, A., Berger, M.: Variétés Kähleriennes compactes. (Lect. Notes Math., Vol. 154). Berlin Heidelberg New York: Springer 1970
Matsushima, Y.: Remarks on Kähler-Einstein manifolds. Nagoya Math. J.46, 161–173 (1972)
O'Neill, B.: The fundamental equations of a submersion. Mich. Math. J.13, 459–469 (1966)
Salamon, S.M.: Topics in four-dimensional Riemannian Geometry. Preprint, Scuola normale Superiore, Pisa (1982)
Sulanke, R., Wintgen, P.: Differentialgeometrie und Faserbündel. DVW Berlin (1972)
Wells, R.O.: Differential analysis on complex manifolds. New York: Prentice-Hall Inc. 1973
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Kirchberg, K.D. Compact six-dimensional Kähler spin manifolds of positive scalar curvature with the smallest possible first eigenvalue of the Dirac operator. Math. Ann. 282, 157–176 (1988). https://doi.org/10.1007/BF01457018
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DOI: https://doi.org/10.1007/BF01457018