Heisenberg群中低余维的内蕴正则曲面
Intrinsic Regular Surfaces of low codimension in Heisenberg groups
摘要：
本文研究了低余维的$\mathbb{H}^n$的内蕴正则子流形及其内蕴参数化的正则性。推广了一个余维$\mathbb{H}$ -正则曲面的一些结果，刻画了作用在海森堡群$\mathbb{H}^n$的两个互补子群之间的一致内禀可微函数$ϕ$，其目标空间的水平维数为$k$，用$1 \leq k \leq n$，根据其分量关于一族非线性向量场$\nabla^{ϕ_j}$的欧氏正则性.此外，我们展示了如何通过识别$ϕ$的固有微分的矩阵的分量来计算$ϕ$的固有图的面积。
英文摘要：
In this paper we study intrinsic regular submanifolds of $\mathbb{H}^n$, of low co-dimension in relation with the regularity of their intrinsic parametrization. We extend some results proved for one co-dimensional $\mathbb{H}$-regular surfaces, characterizing uniformly intrinsic differentiable functions $ϕ$ acting between two complementary subgroups of the Heisenberg group $\mathbb{H}^n$, with target space horizontal of dimension $k$, with $1 \leq k \leq n$, in terms of the Euclidean regularity of its components with respect to a family of non linear vector fields $\nabla^{ϕ_j}$. Moreover, we show how the area of the intrinsic graph of $ϕ$ can be computed through the component of the matrix identifying the intrinsic differential of $ϕ$.
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