Properties of the Dirac spectrum on three dimensional lens spaces

TL;DR

This paper proves that the Dirac spectrum uniquely determines three-dimensional lens spaces, including all homogeneous and prime order cases, highlighting spectral rigidity in geometric analysis.

Contribution

It establishes that the Dirac spectrum completely characterizes three-dimensional lens spaces, including prime order cases, advancing understanding of spectral geometry.

Findings

Dirac spectrum uniquely determines lens spaces

Spectral rigidity holds for all homogeneous lens spaces

Prime order lens spaces are characterized by their Dirac spectrum

Abstract

We present a spectral rigidity result for the Dirac operator on lens spaces. More specifically, we show that each homogeneous lens space and each three dimensional lens space $L(q;p)$ with $q$ prime is completely characterized by its Dirac spectrum in the class of all lens spaces.