Biharmonic maps from a 2-sphere

Abstract

Motivated by the rich theory of harmonic maps from a 2-sphere, we study biharmonic maps from a 2-sphere in this paper. We first derive biharmonic equation for rotationally symmetric maps between rotationally symmetric 2-manifolds. We then apply the equation to obtain a classification of biharmonic maps in a family of rotationally symmetric maps between 2-spheres. We also find many examples of proper biharmonic maps defined locally on a 2-sphere. Our results seem to suggest that any biharmonic map $S^2⟶(N^n,h)$ be a weakly conformal immersion.

18 pages

References in corpus (4)

• Biharmonic PNMC Submanifolds in Spheres
• Biharmonic Riemannian submersions from 3-manifolds
• Biharmonic conformal immersions into 3-dimensional manifolds
• Biharmonic maps into a Riemannian manifold of non-positive curvature

Cited by in corpus (7)

• On f-biharmonic maps and f-biharmonic submanifolds
• Biharmonic and f-biharmonic maps from a 2-sphere
• Reduction methods for the bienergy
• Critical $O(d)$-equivariant biharmonic maps
• Biharmonic maps from tori into a 2-sphere
• A note on equivariant biharmonic maps and stable biharmonic maps
• Biharmonic hypersurfaces in a product space $L^m\times \mathbb{R}$