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- W2965503603 abstract "The theory of harmonic symmetric bilinear forms on a Riemannian manifold is an analogue of the theory of harmonic exterior differential forms on this manifold. To show this, we must consider every symmetric bilinear form on a Riemannian manifold as a one-form with values in the cotangent bundle of this manifold. In this case, there are the exterior differential and codifferential defined on the vector space of these differential one-forms. Then a symmetric bilinear form is said to be harmonic if it is closed and coclosed as a one-form with values in the cotangent bundle of a Riemannian manifold. In the present paper we prove that the kernel of the little known Bourguignon Laplacian is a finite-dimensional vector space of harmonic symmetric bilinear forms on a compact Riemannian manifold. We also prove that every harmonic symmetric bilinear form on a compact Riemannian manifold with non-negative sectional curvature is invariant under parallel translations. In addition, we investigate the spectral properties of the little studied Bourguignon Laplacian." @default.
- W2965503603 created "2019-08-13" @default.
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- W2965503603 date "2019-08-06" @default.
- W2965503603 modified "2023-09-27" @default.
- W2965503603 title "The Bourguignon Laplacian and harmonic symmetric bilinear forms" @default.
- W2965503603 hasPublicationYear "2019" @default.
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