Isospectral nearly Kähler manifolds

Abstract

We give a systematic way to construct almost conjugate pairs of finite subgroups of $Spin(2n+1)$ and $Pin(n)$ for $n\in \mathbb{N}$ sufficiently large. As a geometric application, we give an infinite family of pairs $M_1^{d_n}$ and $M_2^{d_n}$ of nearly Kähler manifolds that are isospectral for the Dirac and Laplace operator with increasing dimensions $d_n>6$. We provide additionally a computation of the volume of (locally) homogeneous six dimensional nearly Kähler manifolds and investigate the existence of Sunada pairs in this dimension.

arXiv commentThis is a revised version in which many corrections were implemented. An extra introductory section was added, and the last part of the paper was rearranged. The paper was accepted for publication in the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg"