Intrinsic regular surfaces of low codimension in Heisenberg groups

Författare

  • Francesca Corni Università di Bologna, Dipartimento di Matematica

Nyckelord:

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

Abstract

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 \(\phi\).

 

Sektion
Articles

Publicerad

2021-06-21

Referera så här

Corni, F. (2021). Intrinsic regular surfaces of low codimension in Heisenberg groups. Annales Fennici Mathematici, 46(1), 79–121. Hämtad från https://afm.journal.fi/article/view/109397