92 research outputs found

    Conformal change of Riemannian metrics and biharmonic maps

    Full text link
    For the reduction ordinary differential equation due to Baird and Kamissoko \cite{BK} for biharmonic maps from a Riemannian manifold (Mm,g)(M^m,g) into another one (Nn,h)(N^n,h), we show that this ODE has no global positive solution for every mβ‰₯5m\geq 5. On the contrary, we show that there exist global positive solutions in the case m=3m=3. As applications, for the the Riemannian product (M3,g)(M^3,g) of the line and a Riemann surface, we construct the new metric g~\widetilde{g} on M3M^3 conformal to gg such that every nontrivial product harmonic map from M3M^3 with respect to the original metric gg must be biharmonic but not harmonic with respect to the new metric g~\widetilde{g}.Comment: 26 pages, 6 figure
    • …
    corecore