Journal of Geometry and Symmetry in Physics

f-biharmonic Maps Between Riemannian Manifolds

Yuan-Jen Chiang

Abstract

We show that if $\psi$ is an $f$-biharmonic map from a compact Riemannian manifold into a Riemannian manifold with non-positive curvature satisfying a condition, then $\psi$ is an $f$-harmonic map. We prove that if the $f$-tension field $\tau_f(\psi)$ of a map $\psi$ of Riemannian manifolds is a Jacobi field and $\phi$ is a totally geodesic map of Riemannian manifolds, then $\tau_f( \phi\circ \psi)$ is a Jacobi field. We finally investigate the stress $f$-bienergy tensor, and relate the divergence of the stress $f$-bienergy of a map $\psi$ of Riemannian manifolds with the Jacobi field of the $\tau_f (\psi)$ of the map.

Article information

Source
J. Geom. Symmetry Phys., Volume 27 (2012), 45-58.

Dates
First available in Project Euclid: 26 May 2017

https://projecteuclid.org/euclid.jgsp/1495764127

Digital Object Identifier
doi:10.7546/jgsp-27-2012-45-58

Mathematical Reviews number (MathSciNet)
MR3026386

Zentralblatt MATH identifier
1267.58012

Citation

Chiang, Yuan-Jen. f-biharmonic Maps Between Riemannian Manifolds. J. Geom. Symmetry Phys. 27 (2012), 45--58. doi:10.7546/jgsp-27-2012-45-58. https://projecteuclid.org/euclid.jgsp/1495764127