• 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 


Classification results for biharmonic submanifolds in spheres
We study biharmonic submanifolds of the Euclidean sphere that satisfy certain geometric properties. We classify: (i) the biharmonic hypersurfaces with at most two distinct principal curvatures; (ii)
Biharmonic submanifolds in spheres
We give some methods to construct examples of nonharmonic biharmonic submanifolds of the unitn-dimensional sphereSn. In the case of curves inSn we solve explicitly the biharmonic equation.
Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds
In this paper we consider eigenvalues of the Dirichlet biharmonic operator on compact Riemannian manifolds with boundary (possibly empty) and prove a general inequality for them. By using this
Sharp Lower Bounds for the First Eigenvalues of the Bi-Laplace Operator
We obtain sharp lower bounds for the first eigenvalue of four types of eigenvalue problem defined by the bi-Laplace operator on compact manifolds with boundary and determine all the eigenvalues and
Some open problems and conjectures on submanifolds of finite type
  • Soochow J. Math. 17
  • 1991
Biharmonic Submanifolds and Biharmonic Maps in Riemannian Geometry
Biharmonic hypersurfaces in hemispheres
In this paper, we consider the Balmus-Montaldo-Oniciuc's conjecture in the case of hemispheres. We prove that a compact non-minimal biharmonic hypersurface in a hemisphere of $S^{n+1}$ must be the
Eigenvalues on Riemannian manifolds, IMPA Mathematical Publications, 29th Brazilian Mathematics Colloquium
  • Rio de Janeiro,
  • 2013
Tangency and harmonicity properties
  • Ph.D. Thesis, Geometry Balkan Press
  • 2003