A note on conformal vector fields and positive curvature (Q1892736)

The author proves the following result. Theorem. On a closed odd-dimensional Riemannian manifold of positive sectional curvature every two commuting conformal vector fields are dependent at least on one point. To prove the theorem the author shows that the existence of two commuting pointwise linearly independent conformal vector fields implies the vanishing of the sectional curvature somewhere.