f-Biharmonic Maps Between Riemannian Manifold

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Journal of Geometry and Symmetry in Physics

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


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