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The Bourguignon Laplacian and Harmonic Symmetric Bilinear Forms

Author

Listed:
  • Vladimir Rovenski

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

  • Sergey Stepanov

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

  • Irina Tsyganok

    (Department of Data Analysis and Financial Technologies, Finance University, Moscow 125993, Russia)

Abstract

In this paper, we study the kernel and spectral properties of the Bourguignon Laplacian on a closed Riemannian manifold, which acts on the space of symmetric bilinear forms (considered as one-forms with values in the cotangent bundle of this manifold). We prove that the kernel of this Laplacian is an infinite-dimensional vector space of harmonic symmetric bilinear forms, in particular, such forms on a closed manifold with quasi-negative sectional curvature are zero. We apply these results to the description of surface geometry.

Suggested Citation

  • Vladimir Rovenski & Sergey Stepanov & Irina Tsyganok, 2020. "The Bourguignon Laplacian and Harmonic Symmetric Bilinear Forms," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:83-:d:305043
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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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