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Metric deformations of curvature

I: Local convex deformations

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Bibliography

  1. Aubin, T., ‘Metriques Riemannienes at Courbure’, J. Diff. Geometry 4 (1970), 383–424.

    Google Scholar 

  2. Berger and Ebin, ‘Some Decompositions of the Space of Symmetric Tensors on a Riemannian Manifold’, J. Diff. Geometry 3 (1961), 379–392.

    Google Scholar 

  3. Bishop and Goldberg, ‘Some Implications of the Generalized Gauss-Bonnet Theorem’, Trans. Am. Math. Soc. 112 (1964), 508–535.

    Google Scholar 

  4. Bishop and O'Neill, ‘Manifolds of Negative Curvature’, Trans. Am. Math. Soc. 145 (1969), 1–49.

    Google Scholar 

  5. Bourguignon, Sentenac and Deschamps, ‘Conjecture de H. Hopf sur les variétés produits’, Ann. Sci. de L'Ecole Normale Superieure (1972), 277–302.

  6. Bourguignon, Deschamps and Sentenac, ‘Quelques variations particulières d'un produit de métriques’, to appear in Ann. Sci. de L'Ecole Normale Superieure.

  7. Cheeger, ‘Finiteness Theorems of Riemannian Manifolds’, Am. J. Math. XCII (1970), 61–74.

    Google Scholar 

  8. Cheeger and Gromoll, ‘The Splitting Theorem for Manifolds of Nonnegative Ricci Curvature’, J. Diff. Geometry 6 (1971), 119–128.

    Google Scholar 

  9. Ebin, ‘The Manifold of Riemannian Metrics’, Proc. of the Symposia in Pure Math. of the A.M.S., Vol. XV: Global Analysis (1970), 11–40.

    Google Scholar 

  10. Ehrlich, ‘Complete Non-positively Curved Negatively Pointed Metrics on S 1 × .S 1 × R 2, preprint, Centre de Mathematiques de l'Ecole Polytechnique, Paris, France

  11. Ehrlich, ‘Continuity Properties of the Injectivity Radius Function’, Compositio Mathematics 29 (1974), 151–178.

    Google Scholar 

  12. Ehrlich, ‘Local Convex Deformations of Ricci and Sectional Curvature of Compact Manifolds’, Proceedings of the A.M.S. Symposium in Differential Geometry 27 (1975), 69–71.

    Google Scholar 

  13. Ehrlich, ‘Local Convex Deformations and Sectional Curvature’, Archiv der Math. 26 (1975), 432–435.

    Google Scholar 

  14. Gromoll, Klingenberg and Meyer, Riemannsche Geometrie im Großen, Springer-Verlag, Lecture Notes in Mathematics, No. 55, 1968.

  15. Gromoll and Meyer, ‘On Complete Open Manifolds of Positive Curvature’, Ann. of Math. 90 (1969), 75–90.

    Google Scholar 

  16. Hitchin, ‘On Compact Four-Dimensional Einstein Manifolds’, J. Diff. Geometry 9 (1974), 435–443.

    Google Scholar 

  17. Preissman, ‘Quelques Proprietes Globales des Espaces de Riemann’, Comm. Math. Helv. 15 (1943), 175–216.

    Google Scholar 

  18. Weinstein, ‘Positively Curved Deformations of Invariant Riemannian Metrics’, Proc. Am. Math. Soc. 26 (1970), 151–152.

    MATH  Google Scholar 

  19. Yau, S.T., ‘Curvature Restrictions on Four Manifolds’, to appear.

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Authors and Affiliations

  1. Mathematisches Institut der Universität Bonn, 53 Bonn, Wegelerstraße 10, Federal Republic of Germany

    Paul Ehrlich

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  1. Paul Ehrlich
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Supported by SFB 40 at Bonn University while paper revised.

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Ehrlich, P. Metric deformations of curvature. Geom Dedicata 5, 1–23 (1976). https://doi.org/10.1007/BF00148134

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  • DOI: https://doi.org/10.1007/BF00148134

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