(11015) f-Biharmonic maps between doubly warped product manifolds

Abstract

In this paper, by applying the first variation formula of $f$-bi-energy given in \cite{OND}, we study $f$-biharmonic maps between doubly warped product manifolds $M\times_{(\mu,\lambda)}N$. Under imposing existence condition concerning proper $f$-biharmonic maps, we derive $f$-biharmonicity's characteristic equations for the inclusion maps: $i_{y_0}:(M,g) \to (M\times_{(\mu,\lambda)} N, \bar g)$,\,$i_{x_0}: (N,h) \to (M\times_{(\mu,\lambda)} N, \bar g)$ and the product maps: $\overline\Psi=\overline{Id_M \times \varphi_N}: M \times_{(\mu,\lambda)} N \to M\times N$,    $\widetilde \Psi=\widetilde{\varphi_M \times Id_N}: M \times_{(\mu,\lambda)} N \to M\times N$ with $\varphi_M\diagup\varphi_N$ being a harmonic map.

• f-biharmonic maps.pdf