Holonomy restrictions from the curvature operator of the second kind

We show that an n-dimensional Riemannian manifold with n-nonnegative or n-nonpositive curvature operator of the second kind has restricted holonomy SO(n) is flat. The result does not depend on completeness and can be improved provided space Einstein Kähler. In particular, if a locally symmetric kind, then it constant curvature. When irreducible this to 3n2n+2n+4-nonnegative 3n2n+2n+4-nonpositive kind.