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

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

2009-12-24

arxiv.org/abs/0912.4806v1

Mathematics

Differential Geometry

Scientific paper

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.

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