Lichnerowicz Laplacian from the point of view of the Bochner technique (Q6569619)

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.