On m -accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry

We consider a Schrödinger-type differential expression ∇ ∗ ∇ + V , where ∇ is a C ∞ -bounded Hermitian connection on a Hermitian vector bundle E of bounded geometry over a manifold of bounded geometry ( M , g ) with positive C ∞ -bounded measure d μ , and V is a locally integrable linear bundle endomorphism. We define a realization of ∇ ∗ ∇ + V in L 2 ( E ) and give a sufficient condition for its m -accretiveness. The proof essentially follows the scheme of T. Kato, but it requires the use of a more general version of Kato's inequality for Bochner Laplacian operator as well as a result on the positivity of solution to a certain differential equation on M .