Laplace Operators in Differential Geometry - Lichnerowicz Laplacian

The Lichnerowicz Laplacian is defined on symmetric tensors by taking to be the symmetrized covariant derivative. The Lichnerowicz Laplacian is then defined by, where is the formal adjoint. The Lichnerowicz Laplacian differs from the usual tensor Laplacian by a Weitzenbock formula involving the Riemann curvature tensor, and has natural applications in the study of Ricci flow and the prescribed Ricci curvature problem.