An example of Lichnerowicz-type Laplacian (Q784494)

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.