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On the Betti and Tachibana Numbers of Compact Einstein Manifolds

Author

Listed:
  • Vladimir Rovenski

    (Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel)

  • Sergey Stepanov

    (Department of Mathematics, Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences, 20, Usievicha Street, 125190 Moscow, Russia)

  • Irina Tsyganok

    (Department of Data Analysis and Financial Technologies, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, Russia)

Abstract

Throughout the history of the study of Einstein manifolds, researchers have sought relationships between the curvature and topology of such manifolds. In this paper, first, we prove that a compact Einstein manifold ( M , g ) with an Einstein constant α > 0 is a homological sphere when the minimum of its sectional curvatures > α / ( n + 2 ) ; in particular, ( M , g ) is a spherical space form when the minimum of its sectional curvatures > α / n . Second, we prove two propositions (similar to the above ones) for Tachibana numbers of a compact Einstein manifold with α < 0 .

Suggested Citation

  • Vladimir Rovenski & Sergey Stepanov & Irina Tsyganok, 2019. "On the Betti and Tachibana Numbers of Compact Einstein Manifolds," Mathematics, MDPI, vol. 7(12), pages 1-6, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1210-:d:295874
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