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Stability of the p-Curvature Positivity under Surgeries and Manifolds with Positive Einstein Tensor

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Abstract

We establish the stability of the class of manifolds with positive p-curvature under surgeries in codimension ≥ p + 3. As a consequence of this result, we first obtain the classification of compact 2-connected manifolds of dimension ≥ 7 with positive Einstein tensor; and secondly the existence of metrics with positive Einstein tensor on any compact, simply connected, non-spin manifold of dimension ≥ 7 whose second homotopy group is isomorphic to Z2.

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References

  1. Besse, A. L.: Einstein Manifolds, Springer-Verlag, Berlin, 1987.

    Google Scholar 

  2. Doubrovine, B., Novikov, S. and Fomenko, A.: Méthodes de la Théorie de l'Homologie, 3ème partie, traduction françaisc, Editions Mir, Moscow, 1987.

  3. Gromov, M. and Lawson, H. B.: The classification of simply connected manifolds of positive scalar curvature, Ann. of Math. 111 (1980), 423-434.

    Google Scholar 

  4. Heintze, E. and Karcher, H.: A general comparison theorem with applications to volume estimates for submanifolds, Ann. Scient. Ec. Norm. Sup., série 4 11 (1978), 451-470.

    Google Scholar 

  5. Hitchin, N.: Harmonic spinors, Adv. Math 14 (1974), 1-55.

    Google Scholar 

  6. Labbi, M. L.: Sur les nombres de Betti des variétés conformément plates, C.R. Acad. Sci. Paris. série I 319 (1994), 77-88.

    Google Scholar 

  7. Labbi, M. L.: Actions des groupes de Lie presques simples et positivité de la p-courbure, Annales de Toulouse, to appear.

  8. Lawson, H. B. and Michelsohn, M. L.: Spin Geometry, Princeton University Press, Princeton, NJ, 1989.

    Google Scholar 

  9. Micallef, M. J. and Moore, J. D.: Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Annals of Math. 127 (1988), 199-227.

    Google Scholar 

  10. Milnor, J.: Lectures on the h-Cobordism Theorem, Princeton University Press, Princeton, NJ, 1965.

    Google Scholar 

  11. Nayatani, S.: Kleinian groups and conformally flat metrics, in Proceedings of the First MSJ International Research Institute on Geometry and Global Analysis, July 12–23, Tohuku University, Sendai, Japan, 1993, pp. 1-9.

    Google Scholar 

  12. Schoen, R. and Yau, S. T.: On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979), 159-183.

    Google Scholar 

  13. Stolz, S.: Simply connected manifolds of positive scalar curvature, Annals of Math. 136 (1992), 511-540.

    Google Scholar 

  14. Wall, C. T. C.: Geometrical connectivity I., J. London Math. Soc. 2(3) (1971), 597-604.

    Google Scholar 

Download references

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  1. Mathematics Section, International Center for Theoretical Physics, P.O. Box 586, 34100, Trieste, Italy

    Mohammed-Larbi Labbi

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  1. Mohammed-Larbi Labbi
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Labbi, ML. Stability of the p-Curvature Positivity under Surgeries and Manifolds with Positive Einstein Tensor. Annals of Global Analysis and Geometry 15, 299–312 (1997). https://doi.org/10.1023/A:1006553611999

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