2022/01/21 by Xueshan Fu, Fu, Xueshan, Seoung Dal Jung +1
Mathematics · #53C12 #57R30 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2201.08544
openalex publication_date 2022/01/21 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
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 ϕ:(M,g,\mathcal F)→ (M', g',\mathcal F') is a critical point of the transversal p-energy functional EB,p. Trivially, (\mathcal F,\mathcal F')2-harmonic map is (\mathcal F,\mathcal F')-harmonic map, which is a critical point of EB. There is another definition of a harmonic map on foliated Riemannian manifolds, called transversally harmonic map, which is a solution of the Euler-Largrange equation τb(ϕ)=0. Two definitions are not equivalent, but if \mathcal F is minimal, then two definitons are equivalent. Firstly, we give the first and second variational formulas for (\mathcal F,\mathcal F')p-harmonic maps. Next, we investigate the generalized Weitzenböck type formula and the Liouville type theorem for (\mathcal F,\mathcal F')p-harmonic map.