The Bourguignon Laplacian and Harmonic Symmetric Bilinear Forms
Open Access
- 3 January 2020
- journal article
- research article
- Published by MDPI AG in Mathematics
- Vol. 8 (1) , 83
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
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