Bieigenfunctions and biharmonic submanifolds in a sphere
Abstract
In this note, we classify biharmonic submanifolds in a sphere defined by bieigenmaps ($\Delta^2 \phi=\lambda \phi$) or buckling eigenmaps ($\Delta^2 \phi=\mu \Delta \phi$). The results can be viewed as generalizations of Takahashi's characterization of minimal submanifolds in a sphere by eigenmaps.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12687
 Bibcode:
 2021arXiv210912687O
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 6 pages