On constructing biharmonic maps and metrics

被引:57
作者
Baird, P [1 ]
Kamissoko, D [1 ]
机构
[1] Univ Bretagne Occidentale, Dept Math, F-29285 Brest, France
关键词
biharmonic map; biharmonic metric; isoparametric function; Einstein manifold;
D O I
10.1023/A:1021213930520
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We construct biharmonic nonharmonic maps between Riemannian manifolds M and N by first making the ansatz that omega: M --> N be a harmonic map and then deforming the metric conformally on M to render omega biharmonic. The deformation will, in general, destroy the harmonicity of omega. We call a metric which renders the identity map biharmonic, a biharmonic metric. On an Einstein manifold, the only conformally equivalent biharmonic metrics are defined by isoparametric functions.
引用
收藏
页码:65 / 75
页数:11
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