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Eigenvalue estimates for Dirac operators coupled to instantons

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Abstract

We prove a sharp lower bound for the first positive eigenvalue of Dirac operators coupled to instantons and discuss the limit case.

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References

  1. Atiyah, M.F.;Hitchin, N.J.;Singer, I.M.: Selfduality in four-dimensional Riemannian Geometry.Proc. R. Soc. London A 362 (1978), 425–461.

    Google Scholar 

  2. Baum, H.;Friedrich, Th.;Grunewald, R.;Kath, I.:Twistors and Killing Spinors on Riemannian Manifolds. Teubner-Texte Math. Bd. 124, Stuttgart/Leipzig 1991.

  3. Bröcker, T.;Dieck, T.t.:Representation Theory of Compact Lie Groups. Springer Verlag, N.Y. 1985.

    Google Scholar 

  4. Friedrich, Th.: A remark on the first eigenvalue of the Dirac operator on 4-dimensional manifolds.Math. Nachr. 102 (1981), 53–56.

    Google Scholar 

  5. Friedrich, Th.: Self-duality of Riemannian Manifolds and Connections. In:Self-dual Riemannian Geometry and Instantons. Teubner-Texte Math. Bd. 34, Leipzig 1981, 56–104.

  6. Henze, R.:Einige Untersuchungen der Eigenwerte des zu einem Zusammenhang assoziierten Dirac-Operators. Diplomarbeit, Humboldt-Universität 1984.

  7. Kobayashi, S.;Nomizu, K.:Foundation of Differential Geometry. Vol II. Interscience Publ., 1969.

  8. Lawson, H.B.;Michelsohn, M.-L.:Spin Geometry. Princeton Univ. Press, 1989.

  9. Wallach, N.R.:Harmonic Analysis on Homogeneous Spaces. M. Decker Inc., N.Y. 1973.

    Google Scholar 

  10. Želobenko, D.P.:Compact Lie groups and their representations. Providence, RI: Amer. Math. Soc. 1973.

    Google Scholar 

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Baum, H. Eigenvalue estimates for Dirac operators coupled to instantons. Ann Glob Anal Geom 12, 193–209 (1994). https://doi.org/10.1007/BF02108297

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  • DOI: https://doi.org/10.1007/BF02108297

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