Classifications and Isolation Phenomena of Bi-Harmonic Maps and Bi-Yang-Mills Fields

Abstract

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 space of non positive curvature are given. Gauge field analogue is shown, indeed, the isolation phenomena of bi-Yang-Mills fields are obtained.