Corpus ID: 237940463

Bi-eigenfunctions and biharmonic submanifolds in a sphere

  title={Bi-eigenfunctions and biharmonic submanifolds in a sphere},
  author={Ye-Lin Ou},
  • Ye-Lin Ou
  • Published 26 September 2021
  • Mathematics
In this note, we classify biharmonic submanifolds in a sphere defined by bieigenmaps (∆φ = λφ) or buckling eigenmaps (∆φ = −μ∆φ). The results can be viewed as generalizations of Takahashi’s characterization of minimal submanifolds in a sphere by eigenmaps. 1. Biharmonic maps and biharmonic subamnifolds Biharmonic maps are maps between Riemannian manifolds φ : (M, g) → (N, h) which are critical points of the bienergy functional 


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