In this paper, we introduce a horizontal F-energy functional for maps from a Riemannian manifold to a Carnot group. The critical maps of this functional are referred to as CC-F-harmonic maps. Under suitable conditions on the Hessian of the distance function and the degree of F(t), we obtain several Liouville-type theorems for CC-F-harmonic maps from some complete Riemannian manifolds to Carnot groups by assuming either growth condition of the horizontal F-energy or an asymptotic condition at the infinity for the maps.

中文翻译：

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CC-F-调和映射到卡诺组的Liouville型定理

在本文中，我们为从黎曼流形到卡诺组的图引入了水平F能量函数。该功能的临界图称为CC - F谐波图。在适当的距离函数和F（t）程度的Hessian条件下，通过假设水平F的任一增长条件，我们从一些完整的黎曼流形到Carnot组，获得了CC - F调和图的几个Liouville型定理能量或地图的无穷远处的渐近条件。