A remark on the Laplacian operator which acts on symmetric tensors

Original · EN

More than forty years ago J. H. Samson has defined the Laplacian Δsym acting on the space of symmetric covariant p-tensors on an n-dimensional Riemannian manifold (M, g). This operator is an analogue of the well known Hodge-de Rham Laplacian Δ which acts on the space of exterior differential p-forms (1 ≤ p ≤ n) on (M, g). In the present paper we will prove that for n > p = 1 the operator Δsym is the Yano rough Laplacian and show its spectrum properties on a compact Riemannian manifold.