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Deformations of Metrics and Biharmonic Maps

Aicha Benkartab, Ahmed Mohammed Cherif (2020)

Communications in Mathematics

We construct biharmonic non-harmonic maps between Riemannian manifolds ( M , g ) and ( N , h ) by first making the ansatz that ϕ : ( M , g ) ( N , h ) be a harmonic map and then deforming the metric on N by h ˜ α = α h + ( 1 - α ) d f d f to render ϕ biharmonic, where f is a smooth function with gradient of constant norm on ( N , h ) and α ( 0 , 1 ) . We construct new examples of biharmonic non-harmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds.

Energy gaps for exponential Yang-Mills fields

Zhen Rong Zhou (2018)

Archivum Mathematicum

In this paper, some inequalities of Simons type for exponential Yang-Mills fields over compact Riemannian manifolds are established, and the energy gaps are obtained.

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