Isospectral nearly K\"ahler manifolds

José J Vásquez

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arXiv · 1607.01897

Isospectral nearly K\"ahler manifolds

José J Vásquez

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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 K\"ahler 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 K\"ahler manifolds and investigate the existence of Sunada pairs in this dimension.

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José J Vásquez. 2016-07-07. Isospectral nearly K\"ahler manifolds. https://arxiv.org/abs/1607.01897

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