Noncommutative potential theory and the sign of the curvature operator in Riemannian geometry

The aim of this work is to show that in any complete Riemannian manifold M, without boundary, the curvature operator is nonnegative if and only if the Dirac Laplacian D2 generates a C*-Markovian semigroup (i.e. a strongly continuous, completely positive, contraction semigroup) on the Cliord C*-algebra of Mor, equivalently, if and only if the quadratic form $\mathcal{E}$D of D2 is a C*-Dirichlet form.