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A local index theorem for non Kähler manifolds

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References

  1. Atiyah, M.F., Bott, R., Patodi, V. K.: On the heat equation and the index theorem. Invent. Math.19, 279–330 (1973)

    Google Scholar 

  2. Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-Duality and four dimensional Riemannian geometry. Proc. Roy. Soc. Lond. A362, 425–461 (1978)

    Google Scholar 

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

    Google Scholar 

  4. Berline, N., Vergne, M.: A computation of the equivariant index of the Dirac operator. Bull. Soc. Math. Fr.113, 305–345 (1985)

    Google Scholar 

  5. Bismut, J.M.: The atiyah-Singer index theorems: a probabilistic approach I. J. Funct. Anal.57, 56–99 (1984)

    Google Scholar 

  6. Bismut, J.M.: Le théorème d'indice local pour des variétés non kählériennes. C. R. Acad. Sci. Paris Sér. I308, 139–142 (1989)

    Google Scholar 

  7. Bismut, J.M.: Analytic torsion and equivariant Bott-Chern currents (to appear)

  8. Bismut, J.M.: Formules de Lichnerowicz et théorème de l'indice. Proceedings of the Conference in honor of A. Lichnerowicz. D. Bernard, Y. Choquet-Bruhat (ed.) Vol. Géom. Diff., pp. 11–31. Travaux en cours Paris: Hermann 1988

    Google Scholar 

  9. Gauduchon, P.: Le théorème de l'excentricité nulle. C.R.A.S. Sér. A285, 387–390 (1977)

    Google Scholar 

  10. Getzler, E.: A short proof of the Atiyah-Singer index theorem. Topology25, 111–117 (1986)

    Google Scholar 

  11. Gilkey, P.: Curvature and the eigenvalues of the Laplacian. Adv. Math.10, 344–382 (1973)

    Google Scholar 

  12. Gilkey, P.: Invariance theory, the heat equation and the Atiyah-Singer index theorem. Washington: Publish or Perish 1984

    Google Scholar 

  13. Hitchin, N.: Harmonic spinors. Adv. Math.14, 1–55 (1974)

    Google Scholar 

  14. Lichnerowicz, A.: Spineurs harmoniques. C. R. Acad. Sci. Paris Sér. A257, 7–9 (1963)

    Google Scholar 

  15. McKean, H., Singer, I.M.: Curvature and the eigenvalues of the Laplacian. J. Differ. Geom.1, 43–69 (1967)

    Google Scholar 

  16. Patodi, V.K.: Curvature and the eigenforms of the Laplacian. J. Differ. Geom.5, 233–249 (1971)

    Google Scholar 

  17. Patodi, V.K.: Analytic proof of the Riemann-Roch-Hirzebruch theorem for Kähler manifolds. J. Differ. Geom.5, 25–283 (1971)

    Google Scholar 

  18. Quillen, D.: Superconnections and the Chern character. Topology24, 89–95 (1985)

    Google Scholar 

  19. Quillen, D.: Determinants of Cauchy-Riemann operators over a Riemann surface. Funct. Anal. Appl.14, 31–34 (1985)

    Google Scholar 

  20. Ray, D.B., Singer, I.M.: Analytic torsion for complex manifolds. Ann. Math.98, 154–177 (1973)

    Google Scholar 

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  1. Département de Mathématique, Université Paris-Sud, F-91405, Orsay, France

    Jean-Michel Bismut

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  1. Jean-Michel Bismut
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This work was written while the author was visiting IHES during the academic, year 1987–1988

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Bismut, JM. A local index theorem for non Kähler manifolds. Math. Ann. 284, 681–699 (1989). https://doi.org/10.1007/BF01443359

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