We construct locally homogeneous six-dimensional nearly Kähler manifolds as quotients of homogeneous nearly Kähler manifolds M by freely acting finite subgroups of Aut 0 (M). We show that non-trivial such groups do only exists if M = S 3 × S 3 . In that case, we classify all freely acting subgroups of Aut 0 (M) = SU(2) × SU(2) × SU(2) of the form A × B, where A ⊂ SU(2) × SU(2) and B ⊂ SU(2).
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.