Intersections of intrinsic submanifolds in the Heisenberg group

TL;DR

This paper demonstrates that in the first Heisenberg group, the intersection of two intrinsic submanifolds with linearly independent horizontal normals forms a continuous curve, using a chain rule based on recent mathematical results.

Contribution

It introduces a new chain rule approach to analyze intersections of intrinsic submanifolds in the Heisenberg group, revealing their local structure as continuous curves.

Findings

Intersections form injective continuous curves

Horizontal normals are linearly independent at intersection

Chain rule facilitates analysis of submanifold intersections

Abstract

In the first Heisenberg group, we show that the intersection of two intrinsic submanifolds with linearly independent horizontal normals locally coincides with the image of an injective continuous curve. The key tool is a chain rule that relies on a recent result by Dafermos.