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VOL. 14 | 2013 f-biharmonic Maps Between Riemannian Manifolds
Yuan-Jen Chiang

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

## 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.

## Information

Published: 1 January 2013
First available in Project Euclid: 13 July 2015

zbMATH: 1382.58013
MathSciNet: MR3183931

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

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Vol. 14 • 1 January 2013