2019/03/25 by Vladimir Rovenski, Rovenski, Vladimir, С. Е. Степанов +4 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG
paper · pdf · doi:10.48550/arxiv.1903.10230
19 pages
arxiv created 2019/03/25 · openalex publication_date 2019/03/25 · arxiv updated 2019/03/26 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28
There are very few general theorems on the kernel of the well-known Lichnerowicz Laplacian. In the present article we consider the geometry of the kernel of this operator restricted to covariant (not necessarily symmetric or skew-symmetric) tensors. Our approach is based on the analytical method, due to Bochner, of proving vanishing theorems for the null space of Laplace operator. In particular, we pay special attention to the kernel of the Lichnerowicz Laplacian on Riemannian symmetric spaces of compact and noncompact types. In conclusion, we give some applications to the theories of infinitesimal Einstein deformations and the stability of Einstein manifolds.