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2012 f-biharmonic Maps Between Riemannian Manifolds
Yuan-Jen Chiang
J. Geom. Symmetry Phys. 27: 45-58 (2012). DOI: 10.7546/jgsp-27-2012-45-58


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.


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Yuan-Jen Chiang. "f-biharmonic Maps Between Riemannian Manifolds." J. Geom. Symmetry Phys. 27 45 - 58, 2012.


Published: 2012
First available in Project Euclid: 26 May 2017

zbMATH: 1267.58012
MathSciNet: MR3026386
Digital Object Identifier: 10.7546/jgsp-27-2012-45-58

Rights: Copyright © 2012 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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