Intrinsic regular surfaces of low codimension in Heisenberg groups

Francesca Corni¹

¹ Università di Bologna, Dipartimento di Matematica

Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 79-121

Résumé

In this paper we study intrinsic regular submanifolds of $\mathbf{H}^n$ of low codimension in relation with the regularity of their intrinsic parametrization. We extend some results proved for $\mathbf{H}$-regular surfaces of codimension 1 to $\mathbf{H}$-regular surfaces of codimension $k$, with $1 \leq k \leq n$. We characterize uniformly intrinsic differentiable functions, $\phi$, acting between two complementary subgroups of the Heisenberg group $\mathbf{H}^n$, with target space horizontal of dimension $k$, in terms of the Euclidean regularity of their components with respect to a family of non linear vector fields $\nabla^{\phi_j}$. Moreover, we show how the area of the intrinsic graph of $\phi$ can be computed in terms of the components of the matrix representing the intrinsic differential of $\phi$.  

Détail

Keywords: Heisenberg groups, H-regular surfaces, intrinsic graphs, intrinsic differentiability