Abstract
Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extension of f-harmonic maps but also an extension of bi-harmonic maps, and that there should exist many examples of proper bi-f-harmonic maps. In order to find some concrete examples of proper bi-f-harmonic maps, we study the basic properties of bi-f-harmonic maps from two directions which are conformal maps between the same dimensional manifolds and some special maps from or into a warped product manifold.
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Supported by Science Research Project of Higher Schools of Guangxi (2015ZD019) and Key Project of Guangxi University for Nationalities (2012MD033).
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Zhao, Cl., Lu, Wj. Bi-f-harmonic map equations on singly warped product manifolds. Appl. Math. J. Chin. Univ. 30, 111–126 (2015). https://doi.org/10.1007/s11766-015-3258-y
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DOI: https://doi.org/10.1007/s11766-015-3258-y