The Bourguignon Laplacian and Harmonic Symmetric Bilinear Forms

Vladimir Rovenski, Sergey Stepanov and Irina Tsyganok
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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

Mathematics, 2020, vol. 8, issue 1, 1-9

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.

Keywords: Riemannian manifold; Bourguignon Laplacian; symmetric bilinear form; harmonic; curvature; spectral theory; vanishing theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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