Harmonic maps on weighted Riemannian foliations
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On foliations, there are two kinds of harmonic maps, that is, transversally harmonic map and $(\mathcal F,\mathcal F')$-harmonic map which are equivalent when the foliation is minimal. In this paper, we study the properties of transversally $f$-harmonic and $(\mathcal F,\mathcal F')_f$-harmonic maps on weighted Riemannian foliations. Here, $f$ is a basic function. And we investigate the relations between transversal stress-energy tensors and transversally $f$-harmonic maps.
Abstract
On foliations, there are two kinds of harmonic maps, that is, transversally harmonic map and $(\mathcal F,\mathcal F')$-harmonic map which are equivalent when the foliation is minimal. In this paper, we study the properties of transversally $f$-harmonic and $(\mathcal F,\mathcal F')_f$-harmonic maps on weighted Riemannian foliations. Here, $f$ is a basic function. And we investigate the relations between transversal stress-energy tensors and transversally $f$-harmonic maps.