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Conformal change of Riemannian metrics and biharmonic maps
- Source :
- Indiana Univ. Math. J. 63 (6), 1631-1657, 2014
- Publication Year :
- 2013
-
Abstract
- For the reduction ordinary differential equation due to Baird and Kamissoko \cite{BK} 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 $\widetilde{g}$.<br />Comment: 26 pages, 6 figures
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Journal :
- Indiana Univ. Math. J. 63 (6), 1631-1657, 2014
- Publication Type :
- Report
- Accession number :
- edsarx.1301.7150
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1512/iumj.2014.63.5424