Conformal change of Riemannian metrics and biharmonic maps Hisashi NaitoHajime Urakawa 58E2053C43harmonic mapsbiharmonic mapsconformal change For the reduction ordinary differential equation due to Baird and Kamissoko [P. Baird and D. Kamissoko, \textit{On constructing biharmonic maps and metrics}, Ann. Global Anal. Geom. \textbf{23} (2003), no. 1, 65--75] for biharmonic maps from a Riemannian manifold $(M^m,g)$ into another one $(N^n,h)$, we show that this ODE has no global positive solution for every $m\geq 5$. On the contrary, we show that there exist global positive solutions in the case $m=3$. As applications, for the the Riemannian product $(M^3,g)$ of the line and a Riemann surface, we construct the new metric $\widetilde{g}$ on $M^3$ conformal to $g$ such that every nontrivial product harmonic map from $M^3$ with respect to the original metric $g$ must be biharmonic but not harmonic with respect to the new metric $\widetilde{g}$. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5424 10.1512/iumj.2014.63.5424 en Indiana Univ. Math. J. 63 (2014) 1631 - 1657 state-of-the-art mathematics http://iumj.org/access/