Codazzi tensors on 2-dimensional spheres (Q1202811)

The author establishes the following theorem: ``If \(A\) is a Codazzi tensor field with \(\text{tr} A=\text{const}\), on a Riemann 2-sphere \((S^ 2,g)\), then \(A={1\over 2}(\text{tr} A)g\).'' Then he gives some geometric applications and a generalization of this theorem for Codazzi tensors with values in a vector bundle.