  Classifications of all biharmonic isoparametric hypersurfaces in the unit
sphere, and all biharmonic homogeneous real hypersurfaces in the complex or
quaternionic projective spaces are shown. Answers in case of bounded geometry
to Chen's conjecture or Caddeo, Montaldo and Piu's one on biharmonic maps into
a manifold of non positive curvature are given. Gauge field analogue is shown,
and the isolation phenomena of bi-Yang-Mills fields are obtained.
