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There are very few general theorems on the kernel of the well-knownLichnerowicz Laplacian. In the present article we consider the geometry of thekernel of this operator restricted to covariant (not necessarily symmetric orskew-symmetric) tensors. Our approach is based on the analytical method, due toBochner, of proving vanishing theorems for the null space of Laplace operator.In particular, we pay special attention to the kernel of the LichnerowiczLaplacian on Riemannian symmetric spaces of compact and noncompact types. Inconclusion, we give some applications to the theories of infinitesimal Einsteindeformations and the stability of Einstein manifolds.

Geometry in the large of the kernel of Lichnerowicz Laplacians and its applications