On a Laplacian which acts on symmetric tensors

2014/06/11 by Josef Mikesh, Mikesh, J., С. Е. Степанов +3
Mathematics · #53C20 #53C21 #53C24 #Advanced Harmonic Analysis Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1406.2829

openalex publication_date 2014/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we show properties of a little-known Laplacian operator acting on symmetric tensors. This operator is an analogue of the well known Hodge-de Rham Laplacian which acts on exterior differential forms. Moreover, this operator admits the Weitzenböck decomposition and we study it using the analytical method, due to Bochner, of proving vanishing theorems for the null space of a Laplace operator admitting a Weitzenböck decomposition and further of estimating its lowest eigenvalue.

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