## Proceedings of the International Conference on Geometry, Integrability and Quantization

### 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

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436795013

Digital Object Identifier
doi:10.7546/giq-14-2013-74-86

Mathematical Reviews number (MathSciNet)
MR3183931

Zentralblatt MATH identifier
1382.58013

#### Citation

Chiang, Yuan-Jen. f-biharmonic Maps Between Riemannian Manifolds. Proceedings of the Fourteenth International Conference on Geometry, Integrability and Quantization, 74--86, Avangard Prima, Sofia, Bulgaria, 2013. doi:10.7546/giq-14-2013-74-86. https://projecteuclid.org/euclid.pgiq/1436795013