92 research outputs found
Conformal change of Riemannian metrics and biharmonic maps
For the reduction ordinary differential equation due to Baird and Kamissoko
\cite{BK} for biharmonic maps from a Riemannian manifold into another
one , we show that this ODE has no global positive solution for every
. On the contrary, we show that there exist global positive solutions
in the case . As applications, for the the Riemannian product of
the line and a Riemann surface, we construct the new metric on
conformal to such that every nontrivial product harmonic map from
with respect to the original metric must be biharmonic but not
harmonic with respect to the new metric .Comment: 26 pages, 6 figure
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