The fundamental and rigidity theorems for pseudohermitian submanifolds in the Heisenberg groups

TL;DR

This paper investigates the geometric properties of pseudohermitian submanifolds in Heisenberg groups, establishing fundamental theorems related to their uniqueness, existence, and rigidity.

Contribution

It provides new fundamental and rigidity theorems for pseudohermitian submanifolds within the Heisenberg groups, advancing understanding of their geometric structure.

Findings

Proved uniqueness and existence theorems for pseudohermitian submanifolds.

Established rigidity theorems demonstrating geometric invariance.

Enhanced the theoretical framework of submanifold geometry in Heisenberg groups.

Abstract

In this paper, we study some basic geometric properties of pseudohermitian submanifolds of the Heisenberg groups. In particular, we obtain the uniqueness and existence theorems, and some rigidity theorems.