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Six-dimensional Riemannian manifolds with a real Killing spinor

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References

  1. Baum, H.: Complete Riemannian manifolds with imaginary Killing spinors. Ann. of Global Anal. and Geom. 7 (1989) 3, 205–226.

    Article  MathSciNet  MATH  Google Scholar 

  2. Friedrich, Th.: Der erste Eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung. Math. Nachr. 97 (1980), 117–146.

    Article  MathSciNet  MATH  Google Scholar 

  3. Friedrich, Th., Grunewald, R.: On thefirst eigenvalue of the Dirac operator on 6-dimensional manifolds. Ann. of Global Anal. and Geom. 3 (1985) 3, 265–273.

    Article  MathSciNet  MATH  Google Scholar 

  4. Friedrich, Th., Kath, I.: Einstein manifolds of dimension 5 with small first eigenvalue of the Dirac operator. J. Diff. Geom. 29 (1989), 263–279.

    MathSciNet  MATH  Google Scholar 

  5. Friedrich, Th., Kath, I.: 7-dimensional compact Riemannian manifolds with Killing spinors. To appear.

  6. Gray, A.: Some examples of almost hermitian manifolds. Illinois J. Math. 10 (1966), 353–366.

    MathSciNet  MATH  Google Scholar 

  7. Gray, A.: Kähler submanifolds of homogeneous almost hermitian manifolds. Tôhoku Math. J. 21 (1969), 190–194.

    Article  MATH  Google Scholar 

  8. Gray, A.: Vector cross products on manifolds. Trans. Amer. Math. Soc. 141 (1969), 465–504.

    Article  MathSciNet  MATH  Google Scholar 

  9. Gray, A.: Nearly Kähler manifolds. J. Diff. Geom. 4 (1970), 283–309.

    MATH  Google Scholar 

  10. Gray, A.: Riemannian manifolds with geodesic symmetries of order 3. J. Diff. Geom. 7 (1972), 343–369.

    MathSciNet  MATH  Google Scholar 

  11. Gray, A.: The structure of nearly Kähler manifolds. Math. Ann. 223 (1976), 233–248.

    Article  MathSciNet  MATH  Google Scholar 

  12. Husemoller, D.: Fibre Bundles. New York 1966.

  13. Hijazi, O.: A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors. Comm. Math. Physics 104 (1986), 151–162.

    Article  MathSciNet  MATH  Google Scholar 

  14. Hijazi, O.: Caracterisation de la sphère par les premiéres valeurs propres de l'opérateur de Dirac en dimension 3, 4, 7 et 8. C. R. Acad. Sc. Paris, Ser. I, 303 (1986) 9, 417–419.

    MathSciNet  MATH  Google Scholar 

  15. Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, Vols. I, II. New York-London: Intersc. Publ. J. Wiley & Sons 1963, 1969.

    MATH  Google Scholar 

  16. Kotōo, S.: Some theorems on almost Kählerian spaces. J. Math. Soc. Japan 12 (1960), 422–433.

    Article  MathSciNet  Google Scholar 

  17. Lichnerowicz, A.: Spin manifolds, Killing spinors and universality of the Hijazi inequality. Letters in Math. Physics 13 (1987), 331–344.

    Article  MathSciNet  MATH  Google Scholar 

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Grunewald, R. Six-dimensional Riemannian manifolds with a real Killing spinor. Ann Glob Anal Geom 8, 43–59 (1990). https://doi.org/10.1007/BF00055017

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