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The Bourguignon Laplacian and Harmonic Symmetric Bilinear Forms

Authors
  • rovenski, vladimir
  • stepanov, sergey
  • tsyganok, irina
Publication Date
Jan 03, 2020
Identifiers
DOI: 10.3390/math8010083
OAI: oai:mdpi.com:/2227-7390/8/1/83/
Source
MDPI
Keywords
Language
English
License
Green
External links

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.

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