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Application of the Generalized Bochner Technique to the Study of Conformally Flat Riemannian Manifolds

Author

Listed:
  • Josef Mikeš

    (Department of Algebra and Geometry, Faculty of Science, Palacky University, 771 46 Olomouc, Czech Republic)

  • Vladimir Rovenski

    (Department of Mathematics, University of Haifa, Mount Carmel, Haifa 3498838, Israel)

  • Sergey Stepanov

    (Department of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, Russia)

  • Irina Tsyganok

    (Department of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, Russia)

Abstract

In this article, we discuss the global aspects of the geometry of locally conformally flat (complete and compact) Riemannian manifolds. In particular, the article reviews and improves some results (e.g., the conditions of compactness and degeneration into spherical or flat space forms) on the geometry “in the large" of locally conformally flat Riemannian manifolds. The results presented here were obtained using the generalized and classical Bochner technique, as well as the Ricci flow.

Suggested Citation

  • Josef Mikeš & Vladimir Rovenski & Sergey Stepanov & Irina Tsyganok, 2021. "Application of the Generalized Bochner Technique to the Study of Conformally Flat Riemannian Manifolds," Mathematics, MDPI, vol. 9(9), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:927-:d:540949
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    Cited by:

    1. Josef Mikeš & Lenka Rýparová & Sergey Stepanov & Irina Tsyganok, 2022. "On the Geometry in the Large of Einstein-like Manifolds," Mathematics, MDPI, vol. 10(13), pages 1-10, June.

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