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On the second cohomology group of a pinched Riemannian manifold

  • Grigorios Tsagas
Article

Summary

Let M be a compact orientable Riemannian manifold of dimension even. We assume that the manifold can carry a metric, which is positively k-pinked. In the present paper some properties of the second cohomology group of such a manifold are obtained, when the number k is greater than a number which depends on the dimension of the manifold. These properties have some applications on the topological product of some special manifolds.

Keywords

Riemannian Manifold Cohomology Group Topological Product Orientable Riemannian Manifold Compact Orientable Riemannian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. [1]
    M. Berger,Sur les variétes (4/23)-pincées de dimension 5, C. R. Acad. Sc. Paris 257, 1963, 4122–4125.zbMATHGoogle Scholar
  2. [2]
    S. Goldberg,Curvature and Homology, Academic Press, New York, 1962.zbMATHGoogle Scholar
  3. [3]
    M. Greenberg,Lectures on Algebraic Topology, W. A. Benjamin INC. 1967.Google Scholar
  4. [4]
    A. Lichnerowicz,Théorie globale des connexions et des groupes d'holonomie, Dunod, Paris, 1955.zbMATHGoogle Scholar
  5. [5]
    —— ——,Géométrie des groupes de trasformations, Dunod, Paris, 1958.Google Scholar
  6. [6]
    M. Obata,Certain couditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan. 14, 1962, pp. 333–340.zbMATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    G. Tsagas,On the cohomology ring of a positively pinched Riemannian manifold of dimension 4, Mathematische Annalen 185, 75–80 (1970).CrossRefzbMATHMathSciNetGoogle Scholar
  8. [8]
    -- --,On the cohomology ring of a pinched Riemannian manifold of even dimension, to appear in the Proceedings of the «Tagung über differentialgeometrie im Grossen », 1969.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1970

Authors and Affiliations

  • Grigorios Tsagas
    • 1
  1. 1.Bonn

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