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The scalar curvature and the spectrum of the Laplacian of spin manifolds

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References

  1. Atiyah, M.F.: Elliptic operators, discrete groups and von-Neumann algebras. Astérisque32/33, 43–72 (1976)

    Google Scholar 

  2. Atiyah, M.F., Singer, I.: The index of elliptic operators. III. Ann. Math.87, 546–604 (1968)

    Google Scholar 

  3. Aubin, T.: Nonlinear analysis on manifolds. Monge-Ampère equations. Berlin Heidelberg New York:Springer 1982

    Google Scholar 

  4. Brooks, R.: The fundamental group and the spectrum of the Laplacian. Comment. Math. Helv.56, 581–598 (1981)

    Google Scholar 

  5. Berline, N., Vergne, M.: A computation of equivarint index of the Dirac operator. Bull. Soc. Math. France113, 305–345 (1985)

    Google Scholar 

  6. Cheeger, J., Gromoll, D.: The splitting theorem for manifolds of non-negative Ricci curvature. J. Differ. Geom.6, 119–128 (1971)

    Google Scholar 

  7. Gromov, M., Lawson, H.B., Jr: Spin and scalar curvature in the presence of a fundamental group, I. Ann. Math.111, 209–230 (1980)

    Google Scholar 

  8. Kazdan, J., Warner, F.: Prescribing curvatures. Proc. Symp. Pure Math.27, (Part. 2), 309–319 (1975)

    Google Scholar 

  9. Lichnerowicz, A.: Spineurs harmoniques. C.R. Acad. Sci. Paris Ser. A-B257, 7–9 (1963)

    Google Scholar 

  10. McKean, H.P.: An upper bound to the spectrum of Δ on a manifold of negative curvature. J. Differ. Geom.4, 359–366 (1970)

    Google Scholar 

  11. Milnor, J.: A note on curvature and the fundamental group. J. Differ. Geom.2, 1–8 (1968)

    Google Scholar 

  12. O'Neill, B.: The fundamental equation of a submersion. Mich. Math. J.13, 459–469 (1966)

    Google Scholar 

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Ono, K. The scalar curvature and the spectrum of the Laplacian of spin manifolds. Math. Ann. 281, 163–168 (1988). https://doi.org/10.1007/BF01449223

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