Aicha Benkartab ; Ahmed Mohammed Cherif - Deformations of Metrics and Biharmonic Maps

cm:9513 - Communications in Mathematics, January 5, 2021, Volume 28 (2020), Issue 3 - https://doi.org/10.2478/cm-2020-0022
Deformations of Metrics and Biharmonic MapsArticle

Authors: Aicha Benkartab ; Ahmed Mohammed Cherif

    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 {\tilde h_\alpha } = \alpha h + \left( {1 - \alpha } \right){\rm{d}}f \otimes {\rm{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.


    Volume: Volume 28 (2020), Issue 3
    Published on: January 5, 2021
    Imported on: May 11, 2022
    Keywords: General Mathematics,[MATH]Mathematics [math]

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