Abstract
In this paper, we study f-harmonicity of some special maps from or into a doubly warped product manifold. First we recall some properties of doubly twisted product manifolds. After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M × μ,λ N can not be proper f-harmonic maps, we use projection maps and product maps to construct nontrivial f-harmonic maps. Thus we obtain some similar results given in [21], such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps. Furthermore, we investigate non-trivial f-harmonicity of the product of two harmonic maps.
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Partially supported by Guangxi Natural Science Foundation (2011GXNSFA018127).
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Lu, Wj. f-Harmonic maps of doubly warped product manifolds. Appl. Math. J. Chin. Univ. 28, 240–252 (2013). https://doi.org/10.1007/s11766-013-2969-1
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DOI: https://doi.org/10.1007/s11766-013-2969-1