Journal of the
Korean Mathematical Society JKMS

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.

Keywords: Weighted foliation, transversal Bakry-\'Emery Ricci tensor, transversally $f$-harmonic map, $(\mathcal F,\mathcal F')_f$-harmonic map, Liouville type theorem, transverse conservation laws

MSC numbers: 53C12, 53C43, 58E20

Supported by: This paper is supported by Research Ability Cultivation Fund for Young Teachers of Shenyang University of Technology (QNPY202209-24), NSFC (No. 11801065) and NRF-2022R1A2C1003278.