The Lichnerowicz Laplacian Acting on Symmetric Tensor Fields — The Bochner Technique Point of View

In this paper, we prove vanishing theorems for the null space of the Laplacian admitting the Weizenböck decomposition and acting on the space of smooth sections of a Riemannian bundle and, in particular, the space of smooth sections of a bundle of symmetric tensors over complete and closed Riemannian manifolds. In addition, we give a general estimate for eigenvalues of the Laplacian admitting the Weizenböck decomposition and acting on the space of smooth sections of a bundle of symmetric tensors over closed Riemannian manifolds.