Biharmonic and f-biharmonic maps from a 2-sphere

Abstract

We study biharmonic maps and f-biharmonic maps from a round sphere $(S^2,g_0)$, the latter maps are equivalent to biharmonic maps from Riemann spheres $(S^2,f^{-1}{g}_0)$. We proved that for rotationally symmetric maps between rotationally symmetric spaces, both biharmonicity and f-biharmonicity reduce to a 2nd order linear ordinary differential equation. As applications, we give a method to produce biharmonic maps and f-biharmonic maps from given biharmonic maps and we construct many examples of biharmonic and f-biharmonic maps from a round sphere $S^2$ and between two round spheres. Our examples include non-conformal proper biharmonic maps $(S^2,f^{-1}{g}_0)⟶S^2$ and $(S^2,f^{-1}{g}_0)⟶S^n$, or non-conformal f-biharmonic maps $(S^2,g_0)⟶S^2$ and $(S^2,g_0)⟶S^n$ from round sphere with two singular points.

17 pages

References in corpus (3)

• On $f$-bi-harmonic maps between Riemannian manifolds
• On f-biharmonic maps and f-biharmonic submanifolds
• Biharmonic maps from a 2-sphere

Cited by in corpus (1)

• f-Biharmonic maps and f-biharmonic submanifolds II