In this paper, we consider critical maps of a horizontal energy functional for maps from a sub-Riemannian manifold to a Riemannian manifold. These critical maps are referred to as subelliptic harmonic maps. In terms of the subelliptic harmonic map heat flow, we investigate the existence problem for subelliptic harmonic maps. Under the assumption that the target Riemannian manifold has non-positive sectional curvature, we prove some Eells–Sampson type existence results for this flow when the source manifold is either a step-2 sub-Riemannian manifold or a step-r sub-Riemannian manifold whose sub-Riemannian structure comes from a tense Riemannian foliation. Finally, some Hartman type results are also established for the flow.

在本文中，我们考虑了从次黎曼流形到黎曼流形的水平能量函数的临界图。这些临界图被称为亚椭圆谐波图。根据次椭圆谐波图的热流，我们研究了次椭圆谐波图的存在问题。下目标黎曼流形具有非正截面曲率的假设下，我们证明了这种流动一些Eells-桑普森型存在的结果，当源歧管可以是一个步骤-2个子黎曼流形或一个步进ř子黎曼流形其次黎曼结构来自紧张的黎曼叶面结构。最后，还为流程建立了一些Hartman类型的结果。