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On f-bi-harmonic maps and bi-f-harmonic maps between Riemannian manifolds

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Abstract

Both bi-harmonic maps and f-harmonic maps have some nice physical motivation and applications. Motivated largely by f-tension field not involving Riemannian curvature tensor, we attempt to formalize some large objects so as to broaden the notions of f-tension field and bi-tension field. We introduce a very large generalization of harmonic maps called f-bi-harmonic maps as the critical points of f-bi-energy functional, and then derive the Euler-Lagrange equation of f-bi-energy functional given by the vanishing of f-bi-tension field. Subsequently, we study some properties of f-bi-harmonic maps between the same dimensional manifolds and give a non-trivial example. Furthermore, we also study the basic properties of f-bi-harmonic maps on a warped product manifold so that we could find some interesting and complicated examples.

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Authors and Affiliations

  1. School of Sciences, Guangxi University for Nationalities, Nanning, 530006, China

    WeiJun Lu

  2. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    WeiJun Lu

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  1. WeiJun Lu
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Correspondence to WeiJun Lu.

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Lu, W. On f-bi-harmonic maps and bi-f-harmonic maps between Riemannian manifolds. Sci. China Math. 58, 1483–1498 (2015). https://doi.org/10.1007/s11425-015-4997-1

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  • DOI: https://doi.org/10.1007/s11425-015-4997-1

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