Lichnerowicz Laplacian from the point of view of the Bochner technique
type: Item
instance of: scholarly article
title: Lichnerowicz Laplacian from the point of view of the Bochner technique
zbMATH Open document ID: 1547.35357
author: I. A. Aleksandrova
author: Sergey E. Stepanov
author: I. I. Tsyganok
published in: Mathematical Notes
publication date: 2024-07-09T00:00:00Z
review text: This is a short but very interesting paper. The Bochner technique is one of the main analytical methods of Riemannian geometry in the large for more than half a century. It is a method for proving vanishing theorems for the kernels of Laplace operators admitting Weitzenböck decomposition and estimating their least eigenvalues. It is confirmed by many examples for complete and closed Riemannian manifolds. In this paper the Laplace operator referred to as the generalized Lichnerowicz Laplacian is studied. Special cases of the generalized Lichnerowicz Laplacian are the canonical Lichnerowicz Laplacian and the Hodge Laplacian. Vanishing theorems for the kernels of Lichnerowicz and Hodge Laplacians on a complete Riemannian manifold are proved, and the eigenvalues of a Lichnerowicz Laplacian on a closed Riemannian manifold are estimated.
reviewed by: Paul Bracken
Mathematics Subject Classification ID: 35J91
zbMATH DE Number: 7878666
zbMATH Keywords: Lichnerowicz Laplacian
zbMATH Keywords: complete Riemannian manifold
zbMATH Keywords: vanishing theorem for Kernel of Laplacian
zbMATH Keywords: estimate of Laplacian eigenvalue
MaRDI profile type: Publication
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DOI: 10.1134/S0001434624030179
description: scientific article; zbMATH DE number 7878666