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 ∈ N sufficiently large. As a geometric application, we give an infinite family of pairs M dn 1 and M dn 2 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.