Bi-harmonic maps and bi-Yang-Mills fields

Abstract

In this paper, we show the first and second variational formulas of biharmonic maps and bi-Yang-Mills fields, and show the first variation formula of k-harmonic maps, and also give an overview of our recent results in [12], i.e., classifications of all biharmonic isoparametric hypersurfaces in the unit sphere, and all biharmonic homogeneous real hypersurfaces in the complex or quaternionic projective spaces, answers in case of bounded geometry to Chen’s conjecture or Caddeo, Montaldo and Piu’s one on biharmonic maps into a space of non positive curvature and the isolation phenomena of bi-Yang-Mills fields.