On critical maps of the horizontal energy functional between Riemannian foliations

2025/04/02 by Chong, Tian, Dong, Yuxin, Huang, Xin +1
#53C12 #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.01498

Abstract

In this paper, we consider critical points of the horizontal energy E_\HH(f) for a smooth map f between two Riemannian foliations. These critical points are referred to as horizontally harmonic maps. In particular, if the maps are foliated, they become transversally harmonic maps. By utilizing the stress-energy tensor, we establish some monotonicity formulas for horizontally harmonic maps from Euclidean spaces, the quotients K_m of Heisenberg groups and also for transversally harmonic maps from Riemannian foliations with appropriate curvature pinching conditions. Finally, we give Jin-type theorems for either horizontally harmonic maps or transversally harmonic maps under some asymptotic conditions at infinity.

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