An example of Lichnerowicz-type Laplacian
type: Item
instance of: scholarly article
title: An example of Lichnerowicz-type Laplacian
zbMATH Open document ID: 1455.53063
author: Josef Mikeš
author: Sergey E. Stepanov
author: Vladimir Yu. Rovenskij
published in: Annals of Global Analysis and Geometry
publication date: 2020-08-03T00:00:00Z
review text: This paper is a study of the Sampson Laplacian \(\Delta_S\) which acts on covariant symmetric tensors on a Riemannian manifold. The operator \(\Delta_S\) was defined by \textit{J. H. Sampson} [Trans. Am. Math. Soc. 177, 141--153 (1973; Zbl 0249.53018)] and is an example of a Lichnerowicz-type Laplacian. In this article, the authors investigate the null space of \(\Delta_S\) and obtain lower bound estimates on the first eigenvalue of \(\Delta_S\) in terms of upper bounds on curvature.
reviewed by: James Hebda
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 7226880
zbMATH Keywords: Sampson Laplacian
zbMATH Keywords: Bochner method
zbMATH Keywords: complete Riemannian manifold
zbMATH Keywords: null space
zbMATH Keywords: vanishing theorem
zbMATH Keywords: eigenvalue
MaRDI profile type: Publication
full work available at URL: s10455-020-09714-9
OpenAlex ID: W3031113967
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DOI: 10.1007/S10455-020-09714-9
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