Linking Integrals on Rank-1-Symmetric Spaces

TL;DR

This paper develops an integral operator that acts as a right inverse to the Cartan differential on rank-one symmetric spaces, extending the classical Gauss linking integral to these more general spaces.

Contribution

It introduces a new integral operator for rank-one symmetric spaces that generalizes the Gauss linking integral beyond space forms.

Findings

Constructed a right inverse of the Cartan differential as an integral operator.

Extended Gauss linking integral to rank-one symmetric spaces.

Provides tools for linking theory in more general geometric contexts.

Abstract

In symmetric spaces of rank one we obtain a right inverse of the Cartan differential on exact differential forms as an integral operator. As a corollary we extend Gauss linking integral beyond space forms.