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arXiv · 2204.12990

On the Dirac spectrum of homogeneous 3-spheres

Jordi Kling·Dorothee Schueth
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Abstract

We show that any two left-invariant metrics on $S^3\cong\operatorname{SU}(2)$ which are isospectral for the associated classical Dirac operator $D$ must be isometric. In the case of left-invariant metrics of positive scalar curvature, we compute and use the smallest eigenvalue of $D^2$. We show analogous results for left-invariant metrics on $\operatorname{SO}(3)=S^3/\{\pm1\}$ for each of its two spin structures.

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Jordi Kling, Dorothee Schueth. 2022-04-27. On the Dirac spectrum of homogeneous 3-spheres. https://arxiv.org/abs/2204.12990

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