Liouville type theorem for (F;F')p-harmonic maps on foliations

Xueshan Fu, Seoung Dal Jung

Published 2022-01-21Version 1

In this paper, we study $(\mathcal F,\mathcal F')_{p}$-harmonic maps between foliated Riemannian manifolds $(M,g,\mathcal F)$ and $(M',g',\mathcal F')$. A $(\mathcal F,\mathcal F')_{p}$-harmonic map $\phi:(M,g,\mathcal F)\to (M', g',\mathcal F')$ is a critical point of the transversal $p$-energy $E_{B,p}(\phi)$, which is a generalization of $(\mathcal F,\mathcal F')$-harmonic map. Precisely, we give the first and second variational formulas for $(\mathcal F,\mathcal F')_{p}$-harmonic maps. We also investigate the generalized Weitzenb\"ock type formula and the Liouville type theorem for $(\mathcal F,\mathcal F')_{p}$-harmonic map.