Cyclic properties of the harmonic sequence of surface in CPn.
We construct biharmonic non-harmonic maps between Riemannian manifolds and by first making the ansatz that be a harmonic map and then deforming the metric on by to render biharmonic, where is a smooth function with gradient of constant norm on and . We construct new examples of biharmonic non-harmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds.
In this paper, some inequalities of Simons type for exponential Yang-Mills fields over compact Riemannian manifolds are established, and the energy gaps are obtained.