Some inequalities on \(| \nabla R|\), \(| \nabla \,Ric|\) and \(| dr|\) in Riemannian manifolds (Q909252)

Let R, Ric, r, \(\nabla\) be the curvature tensor, the Ricci tensor, the scalar curvature and the operator of the covariant differentiation of an n \((>1)\) dimensional Riemannian manifold (M,g). The author gives some inequalities on norms \(| \nabla R|\), \(| \nabla Ric|\) and \(| dr|\). In addition, he obtains an inequality for Codazzi tensors and a certain inequality on \(| \nabla Ric|\) in Kaehlerian manifolds.