The nonexistence theorems for F-harmonic maps and F-Yang–Mills fields

Let M   be an n(n≥3)n(n≥3)-dimensional complete Riemannian manifold with radial curvature K:−a2≤K≤−b2<0K:−a2≤K≤−b2<0 with a≥b>0a≥b>0. In this paper, we consider the F-harmonic maps from M and F-Yang–Mills fields on M  . By the monotonicity formulae, we can prove that (1) If (n−2)b≥(2dF−1)a(n−2)b≥(2dF−1)a, then every F-harmonic map from M to any Riemannian manifold with finite F-energy is constant, which improves the Dong and Wei's result in [3]; (2) If (n−2)b≥(4dF−1)a(n−2)b≥(4dF−1)a, then every F  -Yang–Mills fields R∇R∇ with finite F-Yang–Mills energy vanishes on M, which improves the Dong and Wei's result in [3].